“IN THIS ARTICLE I should like to show, first of all for the simplest case of the (non-relativistic and unperturbed) hydrogen atom, that the usual rule for quantization can be replaced by another requirement in which there is no longer any mention of ‘integers’. The integral property follows, rather, in the same natural way that, say, the number of nodes of a vibrating string must be an integer. The new interpretation can be generalized and, I believe, strikes very deeply into the true nature of the quantization rules.” With these words Erwin Schrödinger began the first paper of his series, “Quantization as a Proper Value Problem”, sent off to the Annalen der Physik at the end of January, 19261. By the end of June he had completed four more major papers developing and applying the concepts and methods of a new wave mechanics that he hoped would be related to classical mechanics in the same way that wave optics is related to geometrical optics. What impressed him most in his elegant theory, perhaps even more than its evident power to treat a wide range of basic atomic problems, was its “naturalness”, its apparently intuitive character for anyone at home in classical physics, and the way in which it seemed to avoid the most perplexing and disturbing features of the existing quantum theory.
For Schrödinger was writing a quarter of a century after Max Planck had broken with the past by introducing energy quanta into physics, in order to explain the black-body radiation law. During those twenty-five years physicists had been confronted with a series of shocking departures from established modes of thought: Planck’s treatment of the energy as a discrete rather than a continuous variable was followed by Einstein’s modest proposals that radiation must be viewed as somehow composed of independent particles of energy and that a quantum theory of matter as well as radiation must be constructed. In 1913 Niels Bohr compounded these heresies in a theory that explicitly denied the validity of electrodynamics for atomic radiation processes and made the frequencies of atomic spectral lines independent of the frequencies of electronic motions within the atom. Bohr’s ideas, strange as they seemed, served as the starting point for a serious and partly successful attempt to construct a theoretical structure that could explain the physical and chemical properties of matter, including the mysterious regularities recorded by the spectroscopists. By the spring of 1925 the theoretical picture had been elaborated by the work of many physicists into a tantalizingly incomplete and confused tangle of successes and failures, so that Wolfgang Pauli, one of the most acute, and most outspoken, of the younger theorists could write to a friend: “Physics is very muddled again at the moment; it is much too hard for me anyway, and I wish I were a movie comedian or something like that and had never heard anything about physics!”2
Within a few months the atmosphere changed abruptly. Werner Heisenberg, in Göttingen, proposed a new approach to the riddles of the quantum theory and this new approach was quickly developed into an elaborate mathematical formalism by Max Born, Pascual Jordan and Heisenberg himself.3 The new theory—called quantum mechanics by its authors but often referred to as matrix mechanics after its principal mathematical technique—gave promise of really providing the beginnings of a consistent quantum theory, for the first time. It did this, however, only at the price of an even sharper and deeper break with the past, giving up any attempt to offer a physical or intuitive picture of the processes whose outcome could be calculated, and requiring that the theory deal only with relations among quantities that could, at least in principle, be observed.
This brief and necessarily oversimplified account may give some impression of the situation in theoretical physics when Schrödinger’s work began to appear in the spring of 1926. I have deliberately emphasized the widespread sense of the strangeness and even the arbitrariness of the quantum theory, because it was just these properties of the theory that Schrödinger was so happy to avoid with his new wave mechanics. This happiness is evident in his papers, and especially in the paper, On the Relationship of the Heisenberg-Born-Jordan Quantum Mechanics to Mine4, in which to his own surprise and joy Schrödinger was able to demonstrate the complete mathematical equivalence of these two theories, so different in their starting point, their method, and their spirit.
Most of the letters in this volume date from the spring of 1926 and give the reactions of Planck, Einstein, and Lorentz to Schrödinger’s ideas. Planck was obviously enraptured by Schrödinger’s work. Always a traditionalist, essentially conservative in his views, despite his having conceived the revolutionary idea of the quantum of energy in 1900, he welcomed just that “natural” or “intuitive” aspect of wave mechanics which so appealed to its creator.
Lorentz’s reaction to Schrödinger’s work is especially remarkable. For many years physicists had always been eager “to hear what Lorentz will say about it” when a new theory was advanced, and, even at seventy-two, he did not disappoint them. His letter of May 27, 1926 consists of a long analysis and critique of Schrödinger’s work in which Lorentz puts his finger on some of the most questionable points: the dispersion of wave packets, the difficulty of interpreting Schrödinger’s waves in a system of more than one particle, and the doubtful aspects of Schrödinger’s proposal that radiation be understood as a kind of beat frequency phenomenon. Lorentz’s letter, Schrödinger’s detailed response, and Lorentz’s rejoinder (see letters 19-21) give a clear picture of the difficulties that worried Schrödinger as he tried to develop his theory further.
It should be pointed out that not all theorists shared the enthusiastic views of Schrödinger and Planck that wave mechanics at last indicated the proper direction for future theory, or even the more temperate opinion of Lorentz that it would be a pity if this did not turn out to be the right direction. Heisenberg was “deeply disturbed” at the attempt to make the wave concepts central in the theory and expressed himself in no uncertain terms in a letter to Pauli: “The more I reflect on the physical part of the Schrödinger theory the more detestable I find it. Schrödinger really simply throws overboard everything in quantum theory: namely, the photoelectric effect, the Franck [-Hertz] collisions, the Stern-Gerlach effect, etc. Then it isn’t hard to make a theory.”5 And, when Schrödinger lectured on his work at Copenhagen in September 1926, Bohr tried very hard to persuade him that the discontinuous transitions were really indispensable; to which Schrödinger responded: “If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory.”6
It was the fate of Schrödinger’s ideas to be absorbed into the new synthesis of the following year, the Copenhagen Interpretation of quantum mechanics, developed principally by Heisenberg and Bohr, and based on Born’s statistical interpretation of the wave function. Schrödinger never liked the Copenhagen Interpretation and, especially in his later years, marshalled his keen insight, vast erudition, and formidable literary ability in a series of sharp attacks on the prevalent views.7 The few letters in this volume that date from the period after 1926 suggest some of his feelings and ideas on this subject. It is no accident that they form a part of his correspondence with Albert Einstein.
Einstein’s first response to Schrödinger’s work (see letter 9) is as characteristic and, in its own way, as remarkable as that of Lorentz. Einstein had apparently misread Schrödinger’s first article, or misremembered it when he thought about it later, and was dissatisfied with the equation he thought to be Schrödinger’s. This equation failed to satisfy two critical but very general properties: the allowed energy values of independent systems ought to be additive and the equation ought not contain the arbitrary integration constant in the energy. Since the equation Einstein thought to be Schrödinger’s did not have these properties, Einstein suggested another that did: it was just the equation that Schrödinger had in fact introduced in his own paper. Schrödinger was delighted and took Einstein’s remarks as providing new evidence for the reasonableness of his method.
Schrödinger’s wave mechanics owed much to Einstein’s earlier work. One usually reads that Schrödinger was inspired by Louis de Broglie’s thesis in which the concept of matter waves was first advanced, but that is hardly an adequate account. It was Einstein’s profound studies of the wave-particle duality for radiation that originally suggested to de Broglie that a corresponding duality should exist for matter. And it is not surprising that it was Einstein who first recognized the importance of de Broglie’s brilliant idea. “Read it,” he said to Max Born of de Broglie’s thesis, “even though it might look crazy, it is absolutely solid.”8 He was also the first to see the implications of de Broglie’s matter waves and to offer new arguments for their existence in his own quantum theory of the ideal gas (the Bose-Einstein gas).9 Schrödinger’s study of this important development in statistical mechanics drew his attention to de Broglie’s work, as he himself pointed out several times in his papers and in his letter to Einstein of April 23, 1926, reproduced here. Without Einstein’s “short but infinitely far-seeing remarks” Schrödinger might never have tried to develop de Broglie’s ideas further into a full fledged wave mechanics.
Neither Schrödinger nor Einstein had ever taken a major part in the development of the “old quantum theory” with its strong emphasis on applying quantum rules to problems of atomic structure and atomic spectra. This fact may not be irrelevant to the distaste that both men later felt and expressed for the Copenhagen Interpretation. Einstein’s often stated opinion that the quantum mechanical description of physical reality could not be considered complete was reinforced by Schrödinger’s clever conceptual experiment involving the “quantum mechanical cat”. (See letters 16-18) Both men felt, rightly or wrongly, that the great majority of their colleagues had chosen the wrong path.
Schrödinger expressed his concern that physics was running “the grave danger of getting severed from its historical background”.10 During the years he spent in Dublin he often lectured and wrote on this theme. I think he would have liked this little collection of his correspondence, this fragment of a critical chapter in the history of science, since he himself liked to quote, with evident approval, these words of Benjamin Farrington: “History is the most fundamental science, for there is no human knowledge which cannot lose its scientific character when men forget the conditions under which it originated, the questions which it answered, and the functions it was created to serve.”10
Martin J. Klein
Case Institute of Technology
Cleveland, Ohio
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1 E. Schrödinger, Annalen der Physik 79 (1926) p. 361
2 M. Fierz and V. F. Weisskopf, editors, Theoretical Physics in the Twentieth Century (New York: Interscience Publishers Inc., 1960) p. 22
3 W. Heisenberg, Zeitschrift für Physik 33 (1925) p. 879. M. Born and P. Jordan, Zeitschrift für Physik 34 (1925) p. 858. M. Bom, W. Heisenberg, and P. Jordan, Zeitschrift für Physik 35 (1926) p. 557
4 E. Schrödinger, Annalen der Physik 79 (1926) p. 734
5 Reference 2, p. 44
6 W. Pauli, Editor, Niels Bohr and the Development of Physics (New York and London: Pergamon Press, 1955) p. 14
7 See the papers collected in E. Schrödinger, What is Life? and Other Scientific Essays (Garden City, New York: Doubleday and Company, 1956)
8 Louis de Broglie, Physicien et Penseur (Paris: Editions Albin Michel, 1953) p. 165
9 See M. J. Klein, Einstein and the Wave-Particle Duality in The Natural Philosopher (New York: Blaisdell Publishing Company, 1964) III pp. 1-49
10 E. Schrödinger, Reference 7, pp. 132-133