Abstract
Quantum mechanics was initially invented because classical mechanics, thermodynamics and electrodynamics provided no means to explain the properties of atoms, electrons, and electromagnetic radiation. Furthermore, it became clear after the introduction of Schrödinger’s equation and the quantization of Maxwell’s equations that we cannot explain any physical property of matter and radiation without the use of quantum theory. We will see a lot of evidence for this in the following chapters. However, in the present chapter we will briefly and selectively review the early experimental observations and discoveries which led to the development of quantum mechanics over a period of intense research between 1900 and 1928.
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- 1.
E. Schrödinger, Annalen Phys. 386, 109 (1926).
- 2.
E. Schrödinger, Annalen Phys. 386, 109 (1926), paragraph on pp. 134–135, sentences 2–4: “\(\psi \overline{\psi }\) is a kind of weight function in the configuration space of the system. The wave mechanical configuration of the system is a superposition of many, strictly speaking of all, kinematically possible point mechanical configurations. Thereby each point mechanical configuration contributes with a certain weight to the true wave mechanical configuration, where the weight is just given by \(\psi \overline{\psi }\).” Of course, a weakness of this early hint at the probability interpretation is the vague reference to a “true wave mechanical configuration”. A clearer formulation of this point was offered by Born essentially simultaneously, see the following reference. While there was (and always has been) agreement on the importance of a probabilistic interpretation, the question of the concept which underlies those probabilities was a contentious point between Schrödinger, who at that time may have preferred to advance a de Broglie type pilot wave interpretation, and Bohr and Born and their particle-wave complementarity interpretation. In the end the complementarity picture prevailed: There are fundamental degrees of freedom with certain quantum numbers. These degrees of freedom are quantal excitations of the vacuum, and mathematically they are described by quantum fields. Depending on the way they are probed, they exhibit wavelike or corpuscular properties. Whether or not to denote these degrees of freedom as particles is a matter of convenience and tradition.
- 3.
M. Born, Z. Phys. 38, 803 (1926).
- 4.
Fourier transformation is reviewed in Section 2.1
- 5.
Examples of the Schrödinger equation with time-dependent potentials will be discussed in Chapter 13 and following chapters.
- 6.
A. Tonomura, J. Endo, T. Matsuda, T. Kawasaski, Amer. J. Phys. 57, 117 (1989).
- 7.
It has been argued that Bohmian mechanics can also explain the Tonomura experiment through a pilot wave interpretation of the wave function. However, Bohmian mechanics has other problems. We will briefly return to Bohmian mechanics in Problem 7.17.
- 8.
U. Sinha, C. Couteau, T. Jennewein, R. Laflamme, G. Weihs, Science 329, 418 (2010).
Bibliography
A. Sommerfeld, Atombau und Spektrallinien, 3rd edn. (Vieweg, Braunschweig, 1922). English translation Atomic Structure and Spectral Lines (Methuen, London, 1923)
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Dick, R. (2016). The Need for Quantum Mechanics. In: Advanced Quantum Mechanics. Graduate Texts in Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-25675-7_1
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DOI: https://doi.org/10.1007/978-3-319-25675-7_1
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