Schrodinger

Biography

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.

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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.

— David C Clary (2022) "Schrodinger in Oxford" Singapore : World Scientific - page 4

University of Vienna

Friedrich Hasenohrl

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.

Wilhelm Wirtinger

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.

Hans Thirring

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 bringin Schrodinger back to Austria from Oxford in 1936 and again from Dublin in 1956.

Franz Exner

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.

Victor Hess

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.

Master Thesis

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.

Arrive at Oxford, Nobel Prize

On the 9th of November 1933, the Austrian theoretical physicist Erwin 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.

— David C Clary (2022) "Schrodinger in Oxford" Singapore : World Scientific - page 1

Wave Mechanics

Electron in the Hydrogen 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.