Abstract
The ad hoc postulates to explain the Hydrogen emission lines, assuming that the atomic system exists only in a set of energy states, were taken with reticence, and the resistance grew when new experimental results, for atoms in magnetic fields, could not be explained based on those postulates. Physicists of the stature of Sommerfeld, Kramers, Heisenberg and Born were involved in different attempts to formalize the quantization phenomenon. Throughout the 1910s and still in the 1920s, many problems were approached using the old quantum theory.
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Notes
- 1.
Arnold Sommerfeld introduced the fine-structure constant in 1916, in his relativistic deviations of the atomic spectral lines in the Bohr model. The first physical interpretation of the fine-structure constant, \(\alpha =e^2/(4\pi \epsilon _o \hbar c)=7.2973525698 10^{-3}\), is the ratio of the velocity of the electron in the first circular orbit of the relativistic Bohr atom to the speed of light in vacuum. It appears naturally in Sommerfeld’s analysis, and determines the size of the splitting or fine-structure of the hydrogenic spectral lines. The same constant appears in other fields of modern physics.
- 2.
M. Born, W. Heisenberg, and P. Jordan, Zeitschrift für Physik, 35, 557(1925] (received November 16, 1925). [English translation in: B. L. van der Waerden, editor, Sources of Quantum Mechanics (Dover Publications, 1968) ISBN 0-486-61881-1].
- 3.
Einstein also proposed similar rules of quantization.
- 4.
We assume here that the Hydrogen nucleus is at rest.
- 5.
A cyclic or ignorable variable does not appear explicitly in the Hamiltonian.
- 6.
In the modern quantum mechanics, the angular momentum is quantized in the same way, but the process of quantization does not pick out a preferred axis. For this reason, the name ‘space quantization’ fell out of favor, and the same phenomenon is now called the quantization of the angular momentum.
- 7.
L. de Broglie, Comptes Rendus, 177, 507 (1923).
- 8.
Recent experiments claim that similar distributions come out when particles are sent one by one.
- 9.
E. Schrödinger, Ann. Phys. 79, 361 (1926).
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Pereyra Padilla, P. (2012). Diffraction, Duality and the Schrödinger Equation. In: Fundamentals of Quantum Physics. Undergraduate Lecture Notes in Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29378-8_2
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DOI: https://doi.org/10.1007/978-3-642-29378-8_2
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