Schrödinger's scientific work

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Schrödinger's scientific work
This is a short account of the scientific life of Erwin Schrödinger, the first Director of the School of Theoretical Physics of the Dublin Institute for Advanced Studies.

Erwin Schrödinger was born in Vienna in 1887. His father Rudolf had a business in linoleum, which was quite successful. This was not his father's main interest, however. He was a botanist by training, and wrote a number of articles on plant genetics.

During his time at the Institute, Erwin Schrödinger gave a series of lectures on the subject "What is Life", speculating about the molecular basis for life. These were to prove very influential in the eventual discovery of the structure of DNA by Francis Crick and James Watson. There is still a letter from Crick to Schrödinger in the Institute, acknowledging this fact. It is likely that Schrödinger was himself stimulated by his father's interests to think about such matters.
Before he discovered the wave equation for which he is famous, Schrödinger was already an established physicist. He had studied in Vienna under Boltzmann's students Fritz Hasenörl and Franz Exner. He became an assistant to Exner in 1910 and wrote papers on a wide range of subjects including magnetism, dielectrics, radioactivity, Brownian motion and X-ray diffraction. Many of these were clearly inspired by Boltzmann's work and were applications of statistical mechanics. In World War I, Schrödinger served as an artillery officer, after which he returned to his post in Vienna. Conditions were difficult in Austria after the war, however, and having just married Annamarie Bertel (Anny), he moved to Germany in 1920. He spent a term in Jena as assistant to Max Wien, then a term at Stuttgart as junior professor, and then a term as professor in Breslau.
In 1921 he accepted the chair in Zürich that had previously been held by Einstein and Von Laue. Here his scientific work flourished. He published papers on a variety of subjects, including general relativity, probability theory and colour vision. His main focus was on atomic theory, however. He began with a systematic review of the theory of specific heats as first elucidated by Einstein in the initial stages of the development of quantum theory, and improved by Debye and by Born and Von Karman in 1912. Schrödinger compared the theory with experiments. He especially highlighted the difficulties with hydrogen, but could only suggest ad hoc solutions for this. (These were in fact nearly correct, but this could not be explained at the time.) The problem was in fact partly experimental and partly theoretical; the latter can only be elucidated using the concept of 'spin'.
He also studied the statistical mechanics of gases. In particular he addressed the well-known Gibbs paradox by trying to apply quantum rules to the translational motion of the gas molecules. Just at that time an article by Einstein appeared introducing a new statistics suggested by Bose. Schrödinger realised that this provided a more satisfactory solution to the Gibbs paradox than previous ad hoc proposals. He argued that the most natural justification for these statistics is to take the analogy with radiation seriously. This gave credence to the waves introduced by De Broglie and he set out to formulate a wave equation for them.

He first attempted a relativistically invariant equation, but concluded that this leads to contradictions. His famous nonrelativistic equation did not have these problems, however, and he was able to solve it for a number of examples. Interestingly, his derivation of the equation takes Hamilton's formulation of classical mechanics as a starting point, which indeed brings out the analogy between particle mechanics and optics. Hamilton was of course Ireland's most famous mathematician and it is curious that events later led to Schrödinger himself moving there.

In the case of the hydrogen atom, Schrödinger showed that for negative energies solutions to the wave equation only exist if these energies correspond exactly with Bohr's energy levels. (Provided the action constant in the equation is set equal to h/2p.) This was immediately recognised as a major breakthrough. Bohr invited him to Copenhagen in order to try to illucidate the relation with the matrix mechanics developed by Heisenberg, Born and Jordan. There were long and extensive debates, which led Schrödinger to complete exhaustion. Eventually, he published a paper in which it is shown that the two formulations are mathematically equivalent.
In 1927 the fifth Solvay conference was held, in which all the main architects of quantum mechanics were present. Schrödinger gave a presentation about his new wave mechanics, mentioning also his first attempt of a relativistic equation, now called the Klein-Gordon equation, and the difficulties with it.

That year he was offered the chair in Berlin, previously held by Planck. Here he enjoyed the stimulus from the scientific exchange with a remarkable number of physicists of the first rank, notably Einstein, Planck and Von Laue. The following year Dirac formulated his new relativistic equation for the electron, which was immediately recognised as a major step forward. There were still problems with negative-energy solutions, however, and Schrödinger set out to study this equation. Thus he discovered that the solutions to the Dirac equation have a peculiar behaviour: the free motion of an electron decomposes into a rectilinear path and a fast oscillation about this path, which he called the "Zitterbewegung" (trembling motion). Einstein, in the mean time began to question the probabilistic interpretation of the wave equation as put forward by Born soon after Schrödinger proposed his equation. His opposition became particularly forceful at the sixth Solvay conference in 1930. Here the famous exchange took place between Einstein and Bohr about a particular thought experiment proposed by Einstein where he claimed that the energy and time of escape of a photon from a box could be determined with arbitrary precision. Bohr refuted his argument using the time-delay of a clock in a gravitational field discovered by Einstein himself as a result of his general theory of relativity. Since then Einstein shifted his position, conceding that the accepted interpretation of quantum mechanics is consistent, but arguing rather that it is incomplete. It seems likely that Schrödinger was encouraged by Einstein's opposition in his own discomfort with the emerging picture of quantum mechanics. Initially, this is not reflected in his papers, however.

From 1931 the political situation in Germany became increasingly precarious. Einstein moved to the newly created Institute for Advanced Study in Princeton in 1932, after several encounters with Abraham Flexner, the architect of the idea of such an institute. In 1933 Hitler came to power. Schrödinger, not being Jewish, was not in immediate danger, but he was principally opposed to the regime and decided to leave Germany himself. He accepted a temporary position in Oxford as Fellow of Magdalen College. This position was negociated by Lindemann, who wanted to improve the quality of physics in Oxford and found the company I.C.I. prepared to support this position financially. Shortly after accepting this position, Schrödinger was informed that he had been awarded the Nobel Prize in Physics together with Dirac. He arrived in England in November 1933 and immediately travelled to Stockholm to accept the prize.
Most of his writings from the period in Oxford are more philosophical in nature. In 1935 the well-known article by Einstein, Podolski and Rosen appeared, criticising the foundations of quantum mechanics on the grounds of its nonlocality. This prompted Schrödinger to write an extensive review of the current status of quantum mechanics, and the measurement process in particular. This sequence of three articles in Die Naturwissenschaften entitled "Die gegenwärtige Situation in der Quantenmechanik" is still very relevant. They contain among other considerations the famous example of Schrödinger's cat, as well as the presently oft quoted concept of "entanglement" ("Verschränkung" in German). He also wrote a more technical note in the Proceedings of the Cambridge Philosophical Society, in which the English term "entanglement" appears. Here he derived a general relation between corresponding variables of two entangled systems.
In 1936 Schrödinger was approached for a professor position at Edinburgh, which was eventually offered to Born instead. He was then offered a professorship in Graz, which he accepted. Austria was also coming increasingly under the influence of national socialism, however, and he was forced to make a declaration of acceptance of the regime in Nature, which was frowned upon abroad. In 1938 he had nevertheless to give up his position. At the same time, Eamon de Valera, who had become Taoiseach of Ireland in 1932, was looking for an eminent scientist to attract for his dream of an Institute for Advanced Study in Ireland modelled on that in Princeton. He had enquired with Whittaker, who was Astronomer Royal in Ireland, to search for suitable candidates. Whittaker had already spoken to Schrödinger in connection with the professorship in Edinburgh, and mentioned his name to de Valera. The latter then requested Whittaker to send a message to Schrödinger asking him if he would be interested in coming to Dublin. De Valera was president of the League of Nations at the time and came to Geneva for a meeting. Schrödinger left Graz in a hurry and travelled to Rome because no visa was required for Italy as it had a pact with Hitler. In Rome, Fermi arranged shelter for him and his wife in the Vatican, where he telephoned de Valera. He then travelled to Geneva, where De Valera had organised his onward journey to Dublin via England. (Later that year, Fermi went to Stockholm to receive the 1938 Nobel Prize for the creation of new elements through neutron bombardment, upon which he also left his country to move to Columbia University in the United States. Here he played a major role in the development of the atomic bomb.)
When Schrödinger arrived in Dublin in 1939, after a short interlude in Belgium in 1938, the Institute had not been officially established yet. He gave a series of advanced lectures on quantum theory at University College Dublin, which were an immediate success, both because of his obvious fame and because of his clear lecturing style. As it was taking longer than anticipated to get the Institute officially established by Government, De Valera organised a temporary professorship for Schrödinger at the Royal Irish Academy. The Establishment Act of the Institute was hotly debated in the Dail, but it eventually passed, and in June 1940 the first Board meeting of the School of Theoretical Physics took place, during which Schrödinger was elected as Director of the School. During his 15-year tenure at the Institute, Schrödinger organised many symposia, where some of the great physicists of the time participated. This was of enormous benefit to the physical community in Ireland. As Ireland was officially neutral in World War II, Dublin was a relatively peaceful place during these turbulent times and Schrödinger could work undisturbed in the stately old house 'Teach Hamilton' in Merrion Square. The atmosphere in the new Institute was excellent. A lively community developed of advanced students ('Scholars') and regular visitors from the nearby universities and abroad. Heitler joined the School of Theoretical Physics as assistant of Schrödinger. After Schrödinger left in 1956, Heitler took over as Director.
Schrödinger's work between 1942 and 1952 concentrated mainly on unified field theory, in a curious parallel with Einstein. He started by studying the nonlinear version of electromagnetism proposed by Born and Infeld. This was an attempt to avoid infinities which were encountered in the emerging Quantum Field Theory developed by Dirac and others. Schrödinger found an alternative formulation of this theory in terms of complex variables. He also made an extensive study of its solutions, considering the mutual influence of two and more light waves on each other, scattering of light by a point charge, and modifications of the black-body radiation law. He then extended this theory to include gravity, motivated by Weyl's suggestion that the crucial concept for General Relativity is not a metric but an affine connection and can be generalised to include electrodynamics. He wrote a series of articles on affine field equations, proposing various modifications until he arrived at his 'final affine field laws' in 1946. Schrödinger himself was very enthusiastic about this work and communicated regularly with Einstein about it. Eventually, both Einstein and Schrödinger had to be disappointed, however, as the progress of field theory took a different course with the development of renormalisation theory by Feynman, Schwinger and Tomonaga and the experimental confirmation of its incredibly accurate predictions.
Schrödinger did not work exclusively on field theory, but also wrote about the philosophy of quantum mechanics and the fundamentals of probability and applications to cosmic ray observations. He gave regular public lectures which were very popular for his great ability to explain difficult concepts in simple terms. Several of these have been published as small booklets. One of these is the famous "What is Life?" mentioned above.

In 1956, Schrödinger returned to Austria after he became ill with bronchitis and asthma. Hans Thirring arranged a chair for him as Emeritus Professor in Vienna. His work rate then diminished due to ill health. He spent his summers in the Tirol, where he finally died in January 1961. The physics community in Ireland, and the Institute in particular, are very indebted to his presence in Ireland, and the immense boost he gave to the level of research taking place here.


For an extensive biography of Schrödinger's life, see Walter Moore: 'Schrödinger, life and thought', Bath Press, Bath 1989. A more elaborate discussion of Schrödinger's work can be found in: WilliamT. Scott: 'Erwin Schrödinger. An Introduction to His Writings', University of Massachusetts Press, 1967. See also the interesting proceedings of the Schrödinger centenary conference in London: ' Schrödinger. Centenary celebration of a polymath.' C. W. Kilminster (ed.), Cambridge University Press, 1987. Schrödinger's complete works (excluding books) were published by the

Österreichischen Akademie der Wissenschaften, Vieweg & Sohn, Braunschwieg/Wiesbaden, 1984.

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