Schrodinger

Schrodinger was born in Vienna on 1887 and entered the University there to read physics in 1906. He worked there as an assistant from 1910 till his war service and again after the war.

Some shorts appointments at Jena, Stuttgart and Breslau led up to his appointment to the chair of theoretical physics in Zurich in 1921. His six papers founding wave mechanics came at the end of his Zurich years, and in 1927 he went to the chair in Berlin, to remain there till the advent of Hitler in 1933.

He chose to leave, though his own position could have been secure. He spent a short and rather unhappy time in Oxford, even though 1933 was also the year in which he shared the Nobel prize with Dirac.

He was offered a chair in Graz in 1936. Believing that there was no real danger of an Anschluss, he accepted, only to have to leave hastily in 1938 for Rome.

In that year he had some preliminary discussions with Eamon de Valera, and in 1940 the Eire Government established the Dublin Institute for Advanced Studies with Schrodinger as Director of the School of Theoretical Physics.

Fifteen fruitful years followed, his last five years were spent in his native land, where he died at Alpbach (Tyrol) on 1961.

— C.W Kilmister (1987) "Schrodinger : Centenary Celebration of a Polymath" Cambridge : Cambridge University Press - page 1.

Schrodinger was born in Austria in 1887 and was educated in Vienna.

He was at the University of Zurich in 1926 where he published his great breakthrough with his wave mechanics. He then went to Berlin to take up the Chair previously held by Max Planck.

With the rise of the Nazis he left Germany and took up a Fellowship at Magdalen College, Oxford in 1933.

He returned to Austria in 1936 but soon had to leave after the Anschluss in 1938.

After short periods back in Oxford and then Belgium, he eventually was appointed to a position at the new Institute for Advanced Studies in Dublin.

He stayed there until 1956 when he moved back to Vienna. He died in 1961.

— David C Clary (2022) "Schrodinger in Oxford" Singapore : World Scientific - page xi

Early Life
Erwin Rudolf Josef Alexander Schrodinger was born on August 12, 1887 in Vienna.

His father, Rudolf, would have preferred a career in science, but he instead took over the family business as the owner of a small factory. His mother was Georgine, and her mother Emily was born in England. Georgine's sister Minnie helped bring Erwin up and he spoke English with her from an early age. Minnie was married to Max Bamberger, who was a Professor of General Chemistry at the Vienna Polytechnic -- which later became eventually the Technical University of Vienna --. Georgine took him to visit members of their family back in Leamington Spa in England. Thus, even as a child, Erwin was exposed to science and to the English way of living.

Erwin was an only child. His family had a large apartment in central Vienna with a view of St. Stephen's Cathedral. The Austro-Hungarian Empire was at its peak and Vienna was the centrepiece. Science, music and the arts were all flourishing with great names such as Boltzmann, Freud, Mahler and Klimt producing their best work.

Erwin started his studies at the Akademisches Gymnasium in Vienna in 1898. This was the oldest secondary school in Vienna with an emphasis on Latin, Greek and German Literature. Mathematics was studied as a minor component. The facilities were very traditional with poor lighting which gave eyesight problems for several children. Erwin had to wear strong glasses from the age of 12.

He graduated from the Gymnasium top of his class and entered the University of Vienna in 1906. Through the work of physicists such as Doppler, Stefan and, most notably, Boltzmann, the University had gained an outstanding reputation for teaching and research in physics in the second half of the 19th century.

University of Vienna
Friedrich Hasenohrl, Schrodinger's lecturer, had studied with Boltzmann and the Dutch Nobel Prize winner Hendrik Lorentz. Hasenohrl was invited to the 1st Solvay Conference in Brussels in 1911 which was also attended by Albert Einstein, Max Planck, Marie Curie and the British physicsist Frederick Lindemann -- who later recruited Schrodinger to the University of Oxford. Hasenohrl was killed in the First World War in 1915.

Through the mathematics course of Professor Wilhelm Wirtinger, Schrodinger mastered in depth the methods of differential equations which would be crucial for his later breakthrough in wave mechanics.

In the University of Vienna, Schrodinger met Hans Thirring. Thirring was one year younger. He had a career in theoretical physics and corresponded with Schrodinger on a very regular basis. He played a key role in bringing Schrodinger back to Austria from Oxford in 1936 and again from Dublin in 1956.

Schrodinger also attended the lectures in practical physics given by the Director of the Physical Chemistry Institute Franz Exner. In Exner's department, important work had been done on synthesizing radium chloride, which was sent to Rutherford in the UK who used the material for discoveries on the structure of the atom. Exner had also been involved in providing uranium compounds used by Marie and Pierre Curie for their work on radioactivity.

Exner trained many eminent physicists, including Victor Hess, who won the Nobel Prize for the discovery of cosmic radiation. Later, Hess became a colleague of Schrodinger's after he had moved to Graz in Austria from Oxford.

Schrodinger performed an experimental project under the supervision of Exner on the conduction of electricity on the surfaces of insulators in moist air. He spoke on this work at a meeting of the Academy of Sciences in Vienna in 1910. His thesis enabled him to be granted the degree of Dr.phil, which nowadays is equivalent to a Master's Degree.

Military Service
Austria-Hungary at that time had a scheme in which young men who had gone through a significant education could volunteer for military training of one year. This enabled them to avoid the three years of compulsory military service. Therefore, in 1910 Schrodinger volunteered for service in the fortress artillery.

Over Christmas, he went on a ski trip with his friend Hans Thirring, who broke his leg and had to leave the military service. This enabled Thirring to take up a vacant assistant post with Hasenohrl. Thus, when Schrodinger passed his military training a year later as a cadet officer and returned to the University, he could not work with Hasenohrl and continued experimental research with Professor Exner and his assitant Fritz Kohlrausch.

However, he concluded that he was not ideally suited for experimental work. By this time, the great experiments in physics were being done in other countries such as France, the UK and Germany. So he turned to doing individual theoretical work on problems of interest to experiment.

Habilitation
The next qualification in his academic career was the Habilitation, which would enable him to give his own lecture courses, for which he was paid. To achieve this, he had to publish his own papers and give a public lecture on his research. He developed a theory for diamagnetism, in which the electric currents associated with the motion of electrons produce an internal magnetic field. But this theory, based on the velocity distribution of the Scottish scientist Maxwell, did not give good agreement with experiment.

Later, there was a great scientific congress in Vienna to which many of the leading scientists of the day were invited to lecture. As he had achieved his Habilitation, Schrodinger was allowed to attend, but did not give a presentation. This was the first time he had seen Albert Einstein, who spoke on his latest ideas on gravitation. This sparked a new interest for Schrodinger, who just a few years later started an intense correspondence with Einstein that lasted throughout their careers.

World War I
The assassination of the Archduke Franz Ferdinand on 28 June 1914 in Sarajevo set in motion the fast sequence of events that led to the First World War. With Vienna as the epicentre of the Austro-Hungarian Empire, mobilization occured at once. Being aged 26 and a reserve in the army, Schrodinger was called up at once as an artillery officer. He was sent to the border with Italy. At that time Italy was still neutral in the war. Schrodinger was highly fortunate as many of his former student colleagues were sent to the great battles of the Russian front, where the Austro-Hungarian army suffered badly.

With is theoretical style of pursuing research, he was still able, during this period, to continue to think about scientific problems without the need for laboratories or libraries. He even managed to complete some scientific papers. One was on the capillary pressure of gas bubbles and another was on the Brownian motion of particles, the theory of which had been pioneered by Einstein.

Italy finally entered the war in May 1915 on the opposing side to Austria. Schrodinger was moved to Gorz near Trieste. Here there was fierce fighting with the losses on both sides in the hundreds of thousands. However, as he was commander of an artillery battery, he did not see very dangerous service himself. His efforts must have been useful as he received a military citation and was promoted to Oberleutnant, the highest lieutenant officer rank. It was around this time that his former teacher Professor Hasenohrl lost his life in an infantry charge in Tyrol.

Later, Schrodinger was then moved back to Vienna to teach a course for anti-aircraft officers. His experience as an artillery officer inspired him to write a paper on the audibility of large explosions. He developed his own classical wave equation for this problem, which would sow the seed for his great work on another wave equation.

Around this time, Schrodinger also published his first paper on quantum theory. Schrodinger wrote a detailed review of the theory of specific heats, to which Planck, Einstein, Debye and Born had all contributed. Schrodinger's review on specific heats was published in the new journal Naturwissenschaften, which covered all the sciences. It was edited by Arnold Berliner and was a German equivalent to the British journal Nature. In due course Schrodinger became a close friend of Berliner, submitted several more papers to his journal and they corresponded frequently.

Schrodinger studied Einstein's general theory of relativity when he was at the Italian front in 1916. This allowed him to write two short papers on the topic on his return to Vienna in 1917.

Schrodinger was building a reputation for himself. He was approached in 1918 by the Franz Joseph University of Czernowitz about an appointment there. Czernowitz was a small city which had been ruled by several different nations and had been occupied by Austria since 1775. However, in the chaos at the war, the city was taken over first by Ukraine and then Romania. This made it impossible for Schrodinger to take up an appointment there.

In the last year of the First World War, the Austro-Hungarian Empire fell apart. Life became very difficult in Vienna. There was runaway inflation. Food became scarce. When the war finished in November 1918, Schrodinger's military pay was stopped. His income from the University was hardly sufficient to support himself. Schrodinger had continued to live in the apartment of his parents, while his father's business had collapsed. This was the first time in his life that Schrodinger had experienced real hardship. Then, in 1919 his father died.

German
At the University of Vienna, replacements for Hasenohrl to the Chair of Theoretical Physics and Exner to the Chair of Experimental Physics were to be made in 1920. The appointments of Gustav Jager and Felix Ehrenhaft, respectively, were disappointing to Schrodinger. But, around this time, he was offered an assistantship with Max Wien at Jena in Germany. The financial situation in Germany was better than Austria and the salary offered was quite attractive. So, even though the position in Jena was not a permanent one, Schrodinger took the major step in April 1920 of moving away from Vienna for the first time.

Just before his move to Jena, Schrodinger married Annemarie "Anny" Bertel. She was aged 23 and Schrodinger 32. Anny was the daughter of a photographer in Salzburg. Schrodinger had known her since she was a teenager.

Despite the severe financial and political problems in the early 1920s, theoretical physicists had become much in demand in German universities, following the great advances in quantum theory & relativity and many positions were opening up. Almost as soon as the newly-wed couple arrived in Jena in April 1920, Schrodinger was offered a permanent a associate professorship at the Hoschschule fur Technik in Stuttgart and he moved there in October.

At this time, Schrodinger's mother had become very ill in Vienna with cancer. The value of his late father's investments and pension had been much reduced by inflation and she had been turned out of their comfortable apartment. This had a major influence on Schrodinger. It did much to make him neurotic about financial security. He was always tempted by an apparently lucrative offer to a new position. So, just six months later, Schrodinger was on the move again to a more senior professorship in Breslau.

Zurich
He was then approached by yet another university, and this time it was major appointment. Einstein, Max von Laue and Peter Debye had all held professorships at the University of Zurich. The officials there were looking to make a new appointment to continue this great tradition in theoretical physics. Schrodinger received a strong reference from his recent colleague Regener who had been impressed by the clarity of Schrodinger's lectures, even though he had moved on from Stuttgart all too quickly. In addition, the faculty at Zurich had noted the breath of his papers, covering many different areas of physics.

Switzerland had avoided the horrors of the First World War. There was no hyperinflation. The salary and pension offered were more attractive than those Schrodinger had been receiving at the German universities. At the relatively young age for a full professor, Zurich was an ideal appointment. Even though he was well aware he had not yet made a research contribution at the very top level. This was Schrodinger's opportunity to settle down and produce his great work.

Arosa
As soon as he started at the University of Zurich in October 1921, Schrodinger became ill with a serious bout of bronchitis. Five appointments in five different cities in two and a half years were taking their toll. Tuberculosis was suspected and he needed to move to a high altitude to recuperate. The Schrodingers went to Arosa, a town in the Swiss Alps.

In Arosa, Schrodinger wrote two papers that continued his progress with quantum theory. The first was on the quantization of vibrations to calculate the specific heats of solids at high temperatures. The second was on the quantized Bohr orbits of an electron. He mentioned the possible need for the use of complex number in the description of the Bohr orbits.

After nine months, Schrodinger was feeling well enough to return to Zurich. As a full professor at the University of Zurich, Schrodinger had to give an inaugural lecture. He chose the title "What is a Natural Law?" In this lecture, he emphasised the statistical nature of matter.

4th Solvay Conference
His rising reputation allowed Schrodinger to be invited to his first Solvay Conference on Physics in 1924. These conferences, supported by the King of Belgium, had become the leading international gathering for the discussion of the very latest developments in physics. The subject was "The electrical conductivity of metals and related topics". Schrodinger did not present a paper. The photograph for this 4th Solvay Conference shows Marie Curie, Ernest Rutherford, Paul Langevin and William H. Bragg in the front row with Schrodinger somewhat nervously appearing in the third row. It would not be very long before Schrodinger would be moved to the first row and indeed his wave mechanics eventually provided a rigorous theory for explaining electrical conductivity.

It should be noted that scientists based in Germany and Austria were not invited to this Solvay meeting due to the tensions still prevailing after the First World War. So there was no Planck, Einstein, Sommerfeld or Born. However, as Schrodinger was based in Switzerland, he did receive an invitation and there was space for him due to the other abstentees.

Schrodinger Equation
Since his convalescence, he often visited Arosa because Schrodinger was inspired by the mountains where he could concentrate without interruption of his work. It was the place where he discovered his equation. This great breakthrough of the Schrodinger equation occured over Christmas 1925 in Arosa. The first communication of Schrodinger on the discovery of his equation seems to be a handwritten letter sent from the Villa Herwig, Arosa to Wilhelm Wien in Munich on 27 December 1925.

"Just now a new atomic theory is niggling me. If only I knew more mathematics! I am very optimistic about this thing and hope that if only I can master the calculations, it will be very fine."

The paper, the first with the Schrodinger equation, rates amongst the greatest publications in the history of science. The new work very soon received acclaim from the most distinguished theoretical physicists.

Max Planck on 2 April 1926 wrote from Berlin :

"I read your article the way an inquisitive child listens in suspense to the solution of a puzzle that he has been bothered about for a long time. I am delighted with the beauties which are evident to the eye."

Einstein wrote on 16 April 1926 to Schrodinger :

"Professor Planck pointed your theory out to me with well-justified enthusiasm. Then, I studied it too with the greatest of interest. The idea of your article shows real genius."

Following his first paper on wave mechanics, and encouraged by the acclaim he had received, Schrodinger went on to publish one new paper on his equation in nearly every month in 1926 until the summer. This was the most intense period for research in his life. In his final paper in the series, Schrodinger proposed a version of his equation in which his wave function depends on time. This paper was his final burst of genius and Schrodinger did not again publish an original paper at this very top level.

World Tour
He worked very energetically to promote his new theory to audiences around the world. In the summer of 1926, he lectured in his old universities of Jena and Stuttgart, and also in Munich and Berlin. The reception to his lecture from the senior scientists in Berlin, including Planck, Einstein, Nernst and von Laue was very favourable. Planck even invited him to a reception in his house.

Schrodinger also received an invitation from Danish scientist Niels Bohr, who had won the Nobel Prize four years before. Bohr met Schrodinger at Copenhagen railway station in October 1296 and could not leave the lecturer alone for several days in intense discussion of the new theory. The strain was too much for him and he took to his bed in Bohr's house. It was the tradition in those days for the host to invite a distinguished speaker to stay at their own house. Bohr could not resist coming to Schrodinger's bedside to continue the discussion.

Schrodinger was aware of the emerging importance of scientific research in the USA. He arranged for the translation of his collected papers on wave mechanics into English. This is a language which Schrodinger spoke perfectly because of his family links. At the end of 1926, he also published a paper in the "Physical Review", an American journal which was fast evolving as a leading journal for all areas of physics. These publications were a break from essentially all of Schrodinger's previous articles which had been published in German journals and in German language.

Just before Christmas in 1926, almost exactly one year after he discovered his equation, Schrodinger and Anny set sail in a French liner to visit the USA for the first time. He kept a rather amusing diary of the trip. The Atlantic crossing took ten days.

The Schrodingers spent several weeks in Madison at the University of Wisconsin, then travelled by train to the California Institute of Technology (Caltech), Pasadena, stopping off at the Grand Canyon on the way. After Pasadena, he took the train via Salt Lake City and over the Rocky Mountains to Denver, on to Chicago and then to MIT and Harvard. Everyone wanted to meet him and he was a celebrity. At one time, he had to give three talks in a 30-hour period. He gave 57 lectures during this three month visit. His trip forward and backward in many cities across the USA had some similarities to the extensive tours given today by modern rock stars.

His final lecture was at Columbia University in New York before taking the boat for the long cruise home.

Berlin
The Friedrich Wilhelm University was the oldest university in Berlin. Max Planck had held the Chair of Theoretical Physics since 1889. He had won the Nobel Prize in 1918 for his discovery of energy quanta and was to retire in 1926. Max von Laue also held a Chair there, and he had won the Nobel Prize for his work on the diffraction of X-rays by crystals. In addition, Albert Einstein had a non teaching professorship being the Director of the Kaiser Wilhelm Institute for Physics in Berlin. He had moved from the ETH Zurich in 1914.

Several person were considered for the Planck's Chair. Sommerfeld had been the most prolific at supervising early career theoretical physicists who had gone on to major academic careers and this made him first choice. However, he did not want to leave Munich. Debye's interests were thought to be more on the experimental side. Heisenberg, although clearly recognized as a genius, was considered to be too young for a major Chair at the age of just 25.

The appointments committee noted Schrodinger's ingenious invention of wave mechanics, his superb lecturing style and his "charming temperament of a South German". He was also very highly rated by Planck who had been so impressed by his first paper on wave mechanics.

Meanwhile, the University of Zurich came back with a counter offer to attempt to retain their star physicst. Anny recalled

The offer in Berlin was very high from the first moment on. So Zurich tried to get a bit more, but it never came the salary which Berlin offered. When it came to the end, they offered him a double-professor at the ETH and at the university, so that both could pay, but even then he wouldn't have had much as he got in Berlin.

The students in Zurich heard about the offer and organised a torchlight processing that ended in front of Schrodinger's house. He and Anny found this very touching.

Schrodinger and Anny moved to Berlin in August 1927. They rented a large apartment at 44 Cunostrasse in Grunewald.

5th Solvay Conference
Not long after his move to Berlin came the 5th Solvay Conference in Brussels. The topic was "Electrons and Photons". Schrodinger was asked to give one of the main lectures. The Conference did much to promote Schrodinger's breakthrough. However, Schrodinger was still not considered senior enough to be placed in the front row of the photograph for the Conference.

Essentially all of those names who had contributed to the recent development of the quantum theory were at this Solvay Conference, including Bohr, Born, de Broglie, Dirac, Heisenberg, Pauli and Schrodinger. As many as 17 of the attendees had won the Nobel Prize or were to be awarded the Prize. The anti-German prejudice that had prevented Einstein and others from attending the Solvay conferences held after the First World War had melted away. The meeting was chaired by Lorentz who Schrodinger had recently met in Pasadena, where Lorentz had mentioned to him that he would be invited to give a lecture at the 5th Solvay Conference. Lorentz died a few months later.

This meeting is often considered the most celebrated of all the Solvay Conferences. The meeting's chair, Lorentz, invited Schrödinger to give a lecture regarding his newly discovered Schrödinger equation. Schrödinger talk at that meeting was entitled "Wave Mechanics". He started off by summarizing the main conclusions from his papers published in 1926. The statistical interpretation of Schrödinger's wave function was a major discussion point. Both Einstein and Bohr were highly prominent in the debate.

Experimental evidence for the new quantum theory was also a topic at the conference. The experiments of Clinton Davission and Lester Germer, in which electrons scattered from the surface of nickel showed a diffraction pattern, and those of Arthur Compton, in which the frequencies of X-rays were changed when scattered by free electrons, supported de Broglie's ideas on wave-particle duality. Of these three American scientists, Compton had been able to make the long boat trip over the Atlantic for the meeting.

There were several comments from the participant of the meeting. Born wrote to the organiser to say it was the most stimulating conference he had ever taken part in. Heisenberg said :

"Through the possibility of exchange between the representatives of different lines of research, this conference has contributed extraordinarily to the clarification of the physical foundations of the quantum theory. It forms, so to speak, the outward completion of the quantum theory."

Paul Dirac from Cambridge was the youngest person to attend this Solvay Meeting at the age of 25. His view of the meeting was

"I listened to the arguments, but I did not join in them, essentially because I was not very much interested. It seemed to me that the foundation of the work of a mathematical physicist is to get the correct equation. That the interpretation of these equations was only of secondary importance."

London - Heitler
On returning to Berlin, Schrodinger was thrown into a major course of lectures covering several areas of physics but with emphasis on electron theory. He was an eloquent and popular lecturer. At that time in Berlin, there was a remarkable range of lectures that the fortunate students could attend. Planck was still lecturing, Lise Meitner gave a course on nuclear physics, Nernst on experimental physics, Ladenburg on spectroscopy, Fritz London on chemical bonding.

In 1926, Fritz London had become aware of Schrodinger's papers. Following Sommerfeld's encouragement and support, he received a grant from the Rockefeller Foundation to work in Zurich with Schrodinger. London arrived in Zurich early in April 1927, when Schrodinger was in the USA. In Zurich, London met Walter Heitler. Just like London, Heitler was also very keen to learn more about Schrodinger's paper and transferred his grant to Zurich.

However, Schrodinger's style was to carry out research on his own. In contrast to Sommerfeld and Born, who ran large research groups, Schrodinger was not interested in supervising the research of students or postdoctoral fellows. Almost as soon as Schrodinger returned to Zurich, Schrodinger was making the arrangements to go to Berlin. Both London and Heitler, finding themselves unsupervised in Zurich, decided instead to collaborate together on extending Schrodinger's theory.

They chose a key problem in chemistry : the bonding of the hydrogen molecule. They wrote down an approximate form for the wave function of this two-electron system in terms of a product of the hydrogen atom wave functions (orbitals) for the electron centered on each atom. This "valence bond" form of the wave function gave some electron density in the region between the two atoms to produce a chemical bond. After some non-trivial calculations, they were able to compute the strength of this chemical bond.

This work was submitted for publication almost exactly one year after the submission of Schrodinger's first paper on wave mechanics. It was the first advance in applying Schrodinger's quantum mechanics to a molecule with more than one electron. It remains a major paper in quantum chemistry.

This work also illustrates well how the application of Schrodinger's theory to molecules with more than one electron, which is what made him so famous to the wide scientific world. It was done by others, and not by Schrodinger himself. He was aware of this important developments and took Fritz London as an assistant when he moved from Zurich to Berlin. Later, he also arranged for Heitler to join his Institute for Advanced Studies in Dublin in 1941, where he eventually took over from Schrodinger as Director. Heitler took up Irish citizenship and was elected a Fellow of the Royal Society.

Pauling
Another young scientist who came to Zurich to work with Schrodinger was the American Linus Pauling. He had won a Guggenheim grant, which enabled him to come to Europe to learn about the new ideas in quantum mechanics in several centres. He stopped off in Munich to see Sommerfeld, visited Born in Gottingen, and then went to Zurich to learn wave mechanics.

Like Heitler and London, Pauling found Schrodinger elusive in Zurich. But he immediately realised the potential of the work of Heitler and London regarding chemical bond. As a chemist, he could see how the Heitler-London valence bond theory could be extended to calculate the structure and properties of many important molecules -- including those of interest in organic chemistry --. In due course, he used this theory to explain the tetrahedral shape of the methane molecule and the strong bonding in aromatic molecules like benzene. His book, "The Nature of the Chemical Bond", brought this research together. Later, he was awarded the Nobel Prize for Chemistry in 1954. Years later, Pauling was also involved with movements to stop nuclear testing. In 1962, he was awarded a second Nobel Prize, this time for Peace.

Fritz London in Berlin
When Fritz London took his Rockefeller grant to Berlin with Schrodinger, he found the appointment surprisingly congenial. He discovered that Schrodinger's attitude of not interfering with his research had the big advantage that he could work independently. London's work with Heitler on chemical bonding was becoming well known. They had received major compliments on it from no less than Heisenberg, von Laue and Born. Taking quantum mechanics beyond the hydrogen molecule proved difficult at that time because of the computations involved. Meanwhile, London found he could simplify the calculations using the powerful methods of group theory. This work became influential.

London also applied a perturbation theory approach to Schrodinger's wave functions to provide a theoretical framework for the long-range dispersion forces between atoms. These "London forces" are significant for the properties of liquids and gases and even for the structures taken up by biological molecules.

Tempting offers to Fritz London came from Born in Gottingen and Sommerfeld in Munich, but he preferred the dynamic scientific scene then prevalent in Berlin, which was at its peak in the late 1920s. He much enjoyed the seminars where the highly promising younger members like himself, Viktor Wisskopf, Max Delbruck, Eugene Wigner and Leo Szilard could present their latest ideas to the great senior physicists present, including Planck, Einstein, Schrodinger, von Laue, and Nernst. With quantum mechanics starting to influence chemistry, researchers such as Michael Polanyi, Lise Meitner and Otto Hahn would also come over from the Kaiser Wilhelm Institute for Chemistry. Afte the seminar, the participants would often adjourn to a local tavern to continue the discussions. Sometimes, the Schrodingers would invite the group back to their apartment for Viennese sausage parties.

"Berlin was the most wonderful and absolutely unique atmosphere for all the scientists. They knew it all and they appreciated it all. One had a bit forgotten the first war, and before the second, so it was absolutely a wonderful time. The theatre was at the height, the music was at the height, and science with all the scientific institutes, the industry. And the most famous colloquium, the Berlin Academy had published lectures which were very famous too. There were lots of friends who came together, not on a special day. It was absolutely a very social life. My husband like it very much indeed. "

- Anne Schrodinger

London
Sir William Henry Bragg had won the Nobel Prize in 1915 with his son William Lawrence Bragg for his work on the diffraction of X-rays by crystals. He had attended the 5th Solvay Conference where he had heard several of the pioneers of the new quantum mechanics speak. He was now the Director of the Royal Institution, in the centre of London.

The Royal Institution had become famous not only through the pioneering experimental research of Humphry Davy and Michael Faraday, but also through the communication of science from lectures to the public. This tradition has continued in great style to the present day. The Royal Institution is based in Albemarle Street at a walkable distance from Buckingham Palace and Downing Street. Members of the Royal family often attended the discourses given on Friday evenings.

Bragg invited Schrodinger to give a course of lectures. Schrodinger was pleased to accept it as it would, for the first time, enable him to speak on wave mechanics to a distinguished English audience. Bragg himself gave a lecture at the Royal Institution in advance of Schrodinger's arrival as a prologue to the talks on wave mechanics and emphasized the wave-particle duality of electrons.

Schrodinger gave four lectures in London on 5,7,12 and 14 March 1928 with the title "Wave Mechanics". Anny accompanied him. Schrodinger did not lecture at a Friday evening discourse. His lectures were too technical for the general public, so they were presented on Mondays and Wednesdays.

Between two of his lectures at the Royal Institution, Schrodinger visited Cambridge. He gave a lecture at the Kapitsa Club in Trinity College on Saturday, 10 March, on "The Physical Meaning of Quantum Mechanics". The Russian physicist Pyotr Kapitsa had started this club to hear the latest developments in physics in an informal setting with blackboard and chalk.

Schrodinger had caught a cold during his visit to Cambridge. He was confined to bed in the house of George Birtwistle. There, Schrodinger was visited by the physicist George P. Thomson who had some exciting new experimental results on electron diffraction. Thomson's results demonstrated experimentally the wave nature of the electron and so were of particular interest to Schrodinger. George Thompson was the son of the great Cambridge physicsist J. J. Thomson, who was awarded for the Nobel Prize for Physics in 1906 for his discovery of the electron.

Schrodinger finished his trip to England by visiting Dr. Frederick Pidduck at Corpus Christi College, Oxford on 15 March. This was his first visit to Oxford after the publication of his 1926 papers.

Leiden
After his visits to London, Cambridge and Oxford, Schrodinger and Anny made their way to Leiden in the Netherlands. There, Paul Ehrenfest, who had taken the Chair of Lorentz, held a lecture series to rival the Kapitsa Club in Cambridge. After a good dinner, Ehrenfest would fire probing questions at the visiting speaker who would be staying in the guest room of his house at 57 Witte Rozenstraat. The speaker would then write their signature on the wall in the hall just outside the guest room. Many of the great theoretical physicists had signed in this way, including Einstein, Planck, Bohr and Dirac. Schrodinger added his signature on 21 March 1928.

Monte Carlo Algorithm
Being so much in demand for lectures did not enhance Schrodinger's scientific productivity for new publications. He produced few papers of notes during the six years he spent in Berlin. His six-month burst of creativity of 1926 was not to be repeated again. He only published two papers in 1928 with just some reviews and short essays in 1929. It is true his annus mirabilis of 1926 was an almost impossible act to follow, but Schrodinger was reluctant to get into the details of extending his theory of wave mechanics in more practical way achieved by others such as Born, London, Heitler and Pauling. In the very competitive scientific atmosphere of Berlin in the late 1920s, this lack of productivity was getting noticed. For example, Leo Szilard said : "Unfortunately, Schroding is doing too much reading and not writing anything".

He did, however, publish a novel idea, in which he compared his Schrodinger equation to the diffusion equation for Brownian motion with an imaginary diffusion coefficient. In the present day, this suggestion has been turned into a very powerful "Diffusion Monte Carlo" algorithm, as the diffusion equatiton can be solved with a simple random walk procedure, which is very easy to apply on modern electronic computers. This approach is enabling the Schrodinger equation to be solved numerically for quite complicated multi-dimensional systems, which are hard to tackle with alternative approaches.

Academy of Science
The Prussian Academy of Sciences was a highly prestigious scientific society based in Berlin. There were just five physicists in the academy in 1929 : Planck, Einstein, von Laue, Warburg and Paschen. Schrodinger was elected that year and was the youngest member aged 42. It was expected that members would write papers for the academy. Schrodinger published two papers in 1930 on Heisenberg's uncertainty relations and on relativistic wave mechanics. The Acadmy would come to play an important role in the political storm that would soon overwhelm German science.

In 1931 Schrodinger was delighted to be elected a member of the Royal Irish Academy. He was well aware of the many distinguished mathematicians and theoretical physisicsts who had come from Ireland including George Boole, William Hamilton, Joseph Larmor, George Stokes and Lord Kelvin. Schrodinger equation built on the work of Hamilton. He often found that the distinguished academies he was elected to would be useful to him in his subsequent career.

Oxford
On the 9th of November 1933, Schrodinger came to Magdalen College in Oxford. He was admitted as a Fellow of the College by the President George Gordon, using Latin phrases requesting Schrodinger to obey the Statutes and Bylaws of the College. Schrodinger replied "Do Fidem", which is translated as "I swear." He then shook the right hands of all the Fellows present and each one said to him, "I wish you joy." The ancient bells then rang from the Magdalen Great Tower. Schrodinger and his new colleagues processed to the High Table in the Hall to celebrate his admission over a fine dinner.

At the end of the dinner, President Gordon was called to his office in the President's Lodgings to receive a telephone call. It was from the Times newspaper saying that the Royal Swedish Academy of Sciences had just announced that Schrodinger had won the Nobel Prize in Physics for 1933, jointly with Paul Dirac from the University of Cambridge. President Gordon then called Schrodinger to his office to inform him of the happy news. Gordon said to Schrodinger, "I think you may believe it as the Times would not say such a thing unless they really know. As for me I was truly astonished as I thought you had won the prize."

In this way, Schrodinger won the Nobel Prize as a Fellow of Magdalen for just a few hours.

One-Electron Hidrogen Atom
Schrodinger was awarded the Nobel Prize for the equation under his own name which he published early in 1926 when he was working at the University of Zurich. In this paper, he wrote down a new equation for the description of the electron in the hydrogen atom. It had the simple form HΨ = EΨ. Here H contains mathematical terms representing both the kinetic energy and the potential energy of the electron. At particular quantised energies, contributions from the kinetic and potential energies cancel to leave just the constant energy E of the electron.

This equation gave a very simple form for the possible energies of the electron of the hydrogen atom in terms of integers describing the different quantum states and fundamental constants associated with the mass and charge of the electron, together with Planck's constant.

This formula for the energy states had been given first by the Danish physicst Niels Bohr, who found it fitted to the results derived by Balmer and Rydberg from the lines they observed experimentally with different colours in the emission spectrum of hydrogen gas. It was not this energy formula, however, that seemed so revolutionary to the scientists of the day, but the wave function Ψ, also denoted by Schrodinger as an "orbital". This new mathematical invention gave very accurately all the other observed properties of the electron, such as the spectrum for electron in the presence of an electric field, an observation known as the Stark effect.

The term "wave mechanics" was given by Schrodinger to his theory because it relates to the work of the French physicist Louis de Broglie who had proposed that the electron has some properties similar to those of a wave. Accordingly, shortly before his discovery, it was suggested to Schrodinger by his Zurich colleague Peter Debye that there ought to be a mathematical equation for the electron describing it as a wave. That is exactly what Schrodinger discovered.

It was easy to write down Schrodinger's equation for any number of electrons and protons, but it was harder to solve it, even in an approximate form, especially for an atom or molecule with more than one electron. However, the idea of the orbital for one electron at once found many uses in the qualitative description of chemical bonding and properties of molecules.

Two-Electron Helium Atom
Niels Bohr had not been successful at extending his own theory to atoms with more than one electron and to molecules. Schrodinger himself did make unpublished attempts to to this with his own theory, but without success. However, he was not aware of the work by Uhlenbeck and Goudsmit, which suggested that an individual electron could have different quantum states that were visualised as the particle spinning clockwise or anticlockwise. When Schrodinger's wave functions were modified to include these spins, the spectrum for the two-electron helium atom was explained, as was the chemical bonding of the hydrogen molecule. Linus Pauling stated, "His great discovery based on an idea, the idea that the properties of atoms and molecules could be calculated by solution of a differential equation."

Positron
Not long after the publication of the first paper by Schrodinger, the Cambridge theoretical physicist Paul Dirac published his own form of quantum mechanics which incorporated the treatment of Einstein's theory of relativity. He predicted a new kind of particle, which was called a positron. This particle had the same properties as an electron, except for an opposite charge. It was observed soon after its prediction.

Follow Ups
In 1926, Schrodinger followed up his paper on the energy levels of the hydrogen atom with four other papers which were published in the Annalen der Physik. He demonstrated that his equation described the harmonic oscillator and rotational motion, which can be identified with the vibrating and rotating states of a diatomic molecule. He also showed that his new quantum theory could be made equivalent to an alternative approach developed a few months before by Heisenberg, Born and Jordan. He developed his theory to show how it applied to the Stark effect. Finally, he derived a second Schrodinger equation in which his wave function depended on time.

Research Style
Schrodinger had received an education which had allowed him to move eventually to a top university in which he could undertake his own research. He had developed his own particular style of finding a problem of interest to experimentalists, proposing an equation to describe the system and finally using rigorous mathematics to find analytical solutions. He did this work completely on his own and not in a research group or even guided by a more senior scientist. Elsewhere, many of the most celebrated theoretical physicsts of the time were emerging from large research groups headed by distinguished professors.

Schrodinger did his research on his own and this enabled him to tackle unique problems in his personal style. He had a good supply of research projects from his close link to the experimental department of Exner. There is a parallel to Paul Dirac at Cambridge University who developed his quantum theory entirely on his own, but was still aware of the great experimental discoveries being made on the structure of the atom at the Cavendish Laboratory in Cambridge.

Schrodinger was no focused just on science and nothing else. He was an avid theatre goer and read very widely in philosophy.