Schrodinger: Difference between revisions

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Schrodinger was born in Austria in 1887 and was educated in Vienna.
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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.
 
=== Extending Schrodinger's Theory ===
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.
 
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.
 
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"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
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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.
 
=== Lectures in London ===
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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 ===
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.
 
=== World War II ===
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Later, Einstein had a major influence on the British attempts to assist the many refugee scientists who left Germany in the 1930s.
 
=== RefugeMoving to Britain ===
Shortly after the Nazis came to power, the Academic Assistance Council was set up in Britain by several notable people, including Lord Rutherford. This Council over the next few years helped over 2,600 academic refugees to come to Britain. As many as 16 later won Nobel Prizes, 74 became Fellows of the Royal Society, and 34 Fellows of the British Academy. Furthermore, after being rescued by Britain, several of these scientific refugees moved on to the USA.
 
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Lindemann wrote back to thank Mackenzie on 22 April 1938. He had an additional worrying query about a letter from Schrodinger published in the German papers. Lindemann was referring to a letter that had been published under Schrodinger's name on 30 March 1938. The local newspaper, the Grazer Tagespost, gave the letter the headline "Acclamation of the Fuhrer : A Leading Scientist offers himself for the Service of Nation and Fatherland". His scientific colleagues in Europe and America felt particularly let down by the statement. Some of his former colleagues and associates never forgave him. He also had to do a lot of explaining with close friends, including Einstein, Born and Dirac, when he met or corresponded with them personally in the years to come. Later, he wrote to Einstein with an explanation : "I hope you did not seriously denounce my subsequent, certainly quite cowardly, behaviour. I wanted to stay free. I couldn't do it without gross hypocrisy".
 
His scientific colleagues in Europe and America felt particularly let down by the statement. Some of his former colleagues and associates never forgave him. He also had to do a lot of explaining with close friends, including Einstein, Born and Dirac, when he met or corresponded with them personally in the years to come. Later, he wrote to Einstein with an explanation : "I hope you did not seriously denounce my subsequent, certainly quite cowardly, behaviour. I wanted to stay free. I couldn't do it without gross hypocrisy".
 
The German Consulate in Graz had also seen Schrodinger's public statement seeming to support Hitler. They had forwarded it to the Department of Foreign Affairs in Berlin. The response came that : "The question of withdrawing his Professorship might still be addressed by the local administration". Finally, Schrodinger received a leater from the dean of University of Vienna :
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On the basis of Sect 4. Paragraph 1 of the ordinance for renovation of the Austrian civil service of 31 May 1938, RGBI.I S. 607, you are dismissed. The dismissal is effective as of the day of arrival of this notice. You have no right to any legal recourse against this dimissal.
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=== Escape from Austria ===
The formal description of the ordinance was "the retirement or dismissal of politically unreliable civil servants." For the first time, the alarm bells were truly ringing in the ears of Schrodinger and Anny. Anny described what happened next.
 
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When the Nazis came to Austria, my husband got several invitations to foreign countries.
 
He was not allowed to get the telegrams himself. They were brought to the university. He was called to the university and he was told : "Of course, you have to refuse. You can't go to Brussels or so." So it was really absolutely like a prison.
 
Only through de Valera we were secured. He knew that we were in danger. But it was absolutely sure he could not write to my husband because everything was censored. So he asked Whittaker to ask born. Born wrote to our friend Professor Richard Bar in Zurich. He told a Dutchman, who then came to Vienna. He came to my mother and told her this important thing. He wrote down in just a few lines that de Valera wanted to create an Institute for Advanced Study and whether he would come, in principle. My mother sent this little piece of paper to Graz. We saw it, we read it three times, and then destroyed it, put it into the fire, and told nobody about it at all.
 
Later, I went with my car with Thirring as far as Munich. I went to Switzerland to Constance. I met our friends there and I told them : "Yes, in principle, he will come. But nothing should be done that will let anybody know that we are going away." My friends wrote that to Born, Born told Whittaker, Whittaker told de Valera.
 
My husband never spoke to de Valera. He Never knew de Valera. Nothing at all. But when this missive came, he was perfectly sure that he must leave Austria at once.
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Eamon de Valera was a prominent Irish politician who had been a commander in the 1916 Dublin Easter Rising. He had been the Taoiseach (Head of Government) of Ireland since 1937. He had graduated from the Royal University of Ireland and taught mathematics at several schools. He had heard about the Institute for Advanced Study in Princeton. He was impressed by the recruitment there of Einstein and Weyl. With the distinguished refugees leaving Germany and Austria in large numbers, he had the vision of creating a similar Institute for Advanced Studies in Ireland through recruitment at the top level.
 
Sir Edmund Whittaker, who Schrodinger had met one year before in Rome when they were made founding members of the Pontifical Academy of Science, was a close friend and advisor to de Valera. He had discussed the idea of the Institute for Advanced Studies in detail with de Valera and was a good choice to act as a go-between from De Valera to Max Born and other quiet and careful contacts.
 
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So in three days we packed everything. Three suitcases, we had nothing more. We left everything in Graz behind, took a return ticket to Rome, because everybody knew us in Graz. We didn't dare to take a taxi, so that they knew what we have got with us. With my car I brought the luggage to the station, and then I brought it back to the garage, and I said that they should wash the car. I never saw the car at all again of course. I never saw the other things either because they were confiscated. And with ten marks in our pocket, we left Graz.
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Schrodinger had to leave all of his personal documents behind when he fled from Austria. This included his Nobel and Max Planck gold medals. They left Graz on 14 September 1938, taking the day-long train ride to Rome. At that time, it was possible to cross the border from Austria to Italy without a visa. Once the Schrodingers arrived in Rome, they headed for the Vatican, where Schrodinger had been received at the Pontifical Academy of Science.
 
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We didn't have the money to pay the porter in Rome. There Fermi told us : "Don't write from Rome because it is already dangerous. It might be censored."
 
From Vatican City, where the Papal Academy is situated, my husband wrote three letters. One was to Lindemann to tell him that we left Graz. One to our friends in Zurich to get us some money, because we had to borrow money from Fermi. The third one to de Valera, who was the President of the League of Nations at that time. That was a Saturday when we posted the letters in Vatican City.
 
On Monday morning we went again to the Academy. After half an hour's time, came a servant who told us that his excellency was wanted at the telephone. The Irish envoy was at telephone and he said de Valera rang up this morning from Geneva. He told him to do everything for us to bring us as soon as possible into Geneva. We should be at the legation in the afternoon and there de Valera would phone.
 
So, we were there. This was the first time my husband heard de Valera speaking. He said that he was glad that we were out of Austria. He also said that we should come to Geneva to discuss a few things. But as soon as possible, we should go to England or Ireland, because there was such a great danger of war in 1938. The Munich Conference, you know.
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The Munich conference was going to be held at the end of September 1938. It involved the leaders of Britain and France, meeting with Hitler and Mussolini. The question was the transfer of the German-speaking Sudeten part of Czechoslovakia to Germany. After much discussion, the transfer was agreed with an international commission to consider the future of other disputed areas. On his return, the British PM Chamberlain famously announced, "Peace for our time." Lord Halifax, who did not go with Chamberlain to Germany, informed the House of Lords that the agreement made was a "lesser of two evils".
 
Anny continued the description of their movements
 
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So de Valera tried to get everything ready for us. We couldn't take any money out of Italy, but he gave us a pound each and gave us first class tickets and off we went. I was quite happy already. I felt already safe, but my husband didn't feel safe at all.
 
In Domodossola they looked at our passports and the luggage. They hardly looked at the luggage at all, but the passports were all right. Then, before we came to Iselle, a carabinieri came into our compartment. He had a piece of paper with our name written on it and we had to leave the compartment with all our luggage. They had looked at our passports. We already had visas for all of Europe because de Valera had said that if we can't go through France, we must go through Spain or Portugal or something.
 
Then, we were asked if we had some money. We said that we had one pound. They thought that we had to smuggle something, because one can't go through Europe on one pound.
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Finally, after another 24-hour train trip, they arrived in Geneva. Schrodinger met with de Valera. Then, they stayed for three days in his hotel and then rode on.
 
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There was a blackout in Switzerland. On the other side of the Rhine, one could see the bright lights of Germany.
 
Trains were overflowing and greatly delayed. In France we passed airports with countless airplanes standing ready. All bridges and tunnels were under military guard.
 
In England in Hyde Park, bomb shelters were being feverishly prepared. Anti-aircraft guns pointed to the sky. Everyone had gas masks. In Paddington, we heard reports about the Four Power Conference in Munich. That day, 80,000 children were evacuated.
 
On the 28 September 1938, we reached Oxford.
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It was becoming clear that, due to his letter seemingly supporting the Fuhrer, Schrodinger was not nearly as welcome in Oxford as he had been. The Schrodingers were fortunate to be able to stay in the spacious house of J.H.C Whitehead. Whitehead and Schrodinger had run their joint seminar in Oxford some three years before and had become good friends.
 
Following his flight from Austria and Italy, Schrodinger had no personal resources except his Nobel money in Sweden. That was not even readily available. With just the small grant from Magdalen to live on in Oxford, the Schrodingers were living almost hand to mouth. However, de Valera remained very enthusiastic and provided funds for Schrodinger to travel to Dublin to meet him.
 
There, De Valera explained that it would take about a year to get the legislation passed through the Irish Parliament to set up the Institute for Advanced Studies. De Valera also had an interest in Celtic Studies. He constructed an Act to "make provision for the establishment and maintenance in Dublin of an Institute for Advanced Studies, consisting a School of Celtic Studies and a School of Theoretical Physics". The strange mix of Celtic Studies and Theoretical Physics was to produce some criticism from the opposition members in the Irish Parliament that would delay the passing of the Act.
 
Things were now very uncertain for Schrodinger and Anny. However, as has frequently been the case in Schrodinger's story when he was unsure about his future, he then received a very welcome letter. This was from the Fondation Francqui in Belgium offering him a Visiting Professorship at the University of Ghent. He at once accepted. As was often his method to announce the next move in his career, Schrodinger arranged for Nature on 31 December 1938 to report :
 
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Professor Erwin Schrodinger has been appointed by the Fondation Francqui as a Visiting Professor for the next six months to a "Chaire Francqui" in the University of Ghent. His address is Laboratory of Physics, Plateaustraat 22, Gand, Belgium.
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=== Moving to Ireland ===
The summer of 1939 was a very tense time for the whole of Europe. Schrodinger was waiting more and more anxiously for the call to come to Dublin. On 1 September, German troops invaded Poland and on 3 September Britain and France declared war on Germany. At that time, Belgium was remaining neutral, but it was very vulnerable and had a border with Germany. Schrodinger still had German nationality that once caused a difficulty with the authorities in Belgium. With the announcement of war, de Valera realised he had to act very quickly. He informed Schrodinger he should come to Dublin as soon as possible, even though his Institute for Advanced Studies had not yet been approved by the Irish Parliament. A temporary professorship was being arranged for him.
 
De Valera's promise to assist with travel permits and visas came through. Schrodinger left Belgium on 4 October 1939. First taking a ferry from Ostend to Dover. After arriving in England, the Schrodinger party then travelled to London, leaving from there at 9 pm to Liverpool, going on to Holyhead in Wales and then taking another boat at 4 am to Dublin.
 
Upon his arrival in Ireland, Schrodinger was being funded on a temporary basis by University College Dublin and the Royal Irish Academy. Irish politics, was volatile. De Valera could easily have lost his position of Taoiseach and his proposed Institute for Advanced Studies. Nevertheless, Schrodinger's reception in Dublin was much more enthusiastic than he had been the case in Oxford. In Dublin, he was an academic superstar who was head and shoulders above other academics in the country in terms of his international repuation.
 
He had developed a popular style of lecturing in almost perfect English and in general terms with no mathematics. He was invited to give many public lectures which were enthusiastically received, advertised and reported in the national Irish press. The Irish Independent on 4 November 1939 reported :
 
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Prof. Erwin Schrodinger, Nobel Prize Winner who formerly held an academic chair in Vienna and was just dismissed from his post by the Nazis, began a course of lectures on the latest form of the Quantum Theory at University College Dublin, yesterday.
 
The lecturer paid a tribute to the work of the late Sir William Rowan Hamilton, Astronomer Royal and former President of the Royal Irish Academy. He had been deeply impressed by his work, he said, long before he had come to Ireland.
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By 1940, the German army had invaded Belgium, the Netherlands and Denmark. Chamberlain had resigned and Winston Churchill had become Prime Minister of Great Britain. The situation was getting critical just over the Irish Sea. Meanwhile, the bill to create the Dublin Institute for Advanced Studies was finally passed by the Irish Parliament on 19 June 1940. The first appointment to be made was Professor Erwin Schrodinger as Senior Professor in the School of Physics. He was also appointed to the Council of the Institute for Advanced Studies. So finally Schrodinger had his permanent appointment in a safe place away from the war ravaging close by in Europe. The annual salary was £1,200. This allowed him to cover the living expenses for himself and his family in reasonable comfort.
 
After a succession of nine moves in 20 years with appointments in Jena, Stuttgart, Breslau, Zurich, Berlin, Oxford, Graz, Ghent and Dublin, he did not anticipate that he would be living in Ireland for as long as 17 years. During his 17 years in Ireland, Schrodinger was hugely popular with the public and with the press. As time moved on, he chose more and more general title for his public lectures such as "What is Life", "Science at Play", and "Fun in Science". They were sell-outs. He had become the public face of science in Ireland. Every new prize, election to an academy, new appointment or Honorary Degree, was reported in complementary terms in the "Irish Press".
 
De Valera himself had founded the "Irish Press" newspaper, which always reported very positively on the Taoiseach and his colleagues. Accordingly, Schrodinger was regularly asked by the Irish Press to comment on almost any subject. Even when he went on cycling holidays, it was reported in the press. It seems that any movement he made or any comment he expressed was reported. There were non-sensational reports on his life at home with his family with no difficult questions asked. After the Second World War, he was also in regular demand to speak on highly serious topics such as the nuclear bomb, or how to deal with German or Austrian Nazis.
 
== Wave Mechanics ==