Old quantum theory information

The old quantum theory is a collection of results from the years 1900–1925^[1] which predate modern quantum mechanics. The theory was never complete or self-consistent, but was instead a set of heuristic corrections to classical mechanics.^[2] The theory has come to be understood as the semi-classical approximation^[3] to modern quantum mechanics.^[4] The main and final accomplishments of the old quantum theory were the determination of the modern form of the periodic table by Edmund Stoner and the Pauli exclusion principle which were both premised on the Arnold Sommerfeld enhancements to the Bohr model of the atom.^[5]^[6]

The main tool of the old quantum theory was the Bohr–Sommerfeld quantization condition, a procedure for selection of certain allowed states of a classical system: the system can then only exist in one of the allowed states and not in any other state.

^ Pais, Abraham (2005). Subtle is the Lord: The Science and the Life of Albert Einstein (illustrated ed.). OUP Oxford. p. 28. ISBN 978-0-19-280672-7. Extract of page 28
^ ter Haar, D. (1967). The Old Quantum Theory. Pergamon Press. pp. 206. ISBN 978-0-08-012101-7.
^ Semi-classical approximation. Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-classical_approximation
^ Sakurai, Napolitano (2014). "Quantum Dynamics". Modern Quantum Mechanics. Pearson. ISBN 978-1-292-02410-3.
^ Kragh, Helge (1979). "Niels Bohr's Second Atomic Theory". Historical Studies in the Physical Sciences. 10: 123–186. doi:10.2307/27757389. JSTOR 27757389.
^ Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.7.

[1] Pais, Abraham (2005). Subtle is the Lord: The Science and the Life of Albert Einstein (illustrated ed.). OUP Oxford. p. 28. ISBN 978-0-19-280672-7. Extract of page 28

[2] ter Haar, D. (1967). The Old Quantum Theory. Pergamon Press. pp. 206. ISBN 978-0-08-012101-7.

[3] Semi-classical approximation. Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Semi-classical_approximation

[4] Sakurai, Napolitano (2014). "Quantum Dynamics". Modern Quantum Mechanics. Pearson. ISBN 978-1-292-02410-3.

[5] Kragh, Helge (1979). "Niels Bohr's Second Atomic Theory". Historical Studies in the Physical Sciences. 10: 123–186. doi:10.2307/27757389. JSTOR 27757389.

[6] Kumar, Manjit. Quantum: Einstein, Bohr, and the great debate about the nature of reality / Manjit Kumar.—1st American ed., 2008. Chap.7.

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$i\hbar {\frac {d}{dt}}\|\Psi \rangle ={\hat {H}}\|\Psi \rangle$ Schrödinger equation
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