Deformed quantum mechanics and the Landau problem

Modern Physics Letters A ◽

10.1142/s0217732321501261 ◽

2021 ◽

pp. 2150126

Author(s):

J. Gamboa ◽

F. Méndez

Keyword(s):

Quantum Mechanics ◽

Zeeman Effect ◽

Effect Data ◽

Landau Hamiltonian ◽

Quadratic Zeeman Effect

A deformation of the Landau problem based on a modification of Fock algebra is considered. Systems with the Hamiltonians [Formula: see text] where [Formula: see text] is the Landau Hamiltonian in the lowest level are discussed. The case [Formula: see text] is studied and it is shown that in this particular example, parameters of the problem can be fixed by using the quadratic Zeeman effect data and the Breit–Rabi formula.

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THE THEORY OF THE QUADRATIC ZEEMAN EFFECT

Le Journal de Physique Colloques ◽

10.1051/jphyscol:1970411 ◽

1970 ◽

Vol 31 (C4) ◽

pp. C4-71-C4-74 ◽

Cited By ~ 62

Author(s):

A. R. EDMONDS

Keyword(s):

Zeeman Effect ◽

Quadratic Zeeman Effect

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Constructing Quantum Mechanics

10.1093/oso/9780198845478.001.0001 ◽

2019 ◽

Author(s):

Anthony Duncan ◽

Michel Janssen

Keyword(s):

Quantum Mechanics ◽

Quantum Theory ◽

Stark Effect ◽

Zeeman Effect ◽

Black Body ◽

Black Body Radiation ◽

Wave Mechanics ◽

Specific Heats ◽

Old Quantum Theory ◽

Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

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