On Invariant Vectors in the Presence of Electric and Magnetic Fields

In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace–Runge–Lenz vector, the Redmond vector in the presence of an electric field, the Landau–Avron–Sivardièrevector when the system is subject to a magnetic field, and the supergeneralized...

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Bibliographic Details
Published inAtoms Vol. 11; no. 7; p. 105
Main Author Pain, Jean-Christophe
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2023
Subjects
Atomic physics
Charged particles
dynamical symmetry
Electric fields
Electromagnetic fields
Energy
Hermann–Bernoulli–Laplace–Runge–Lenz vector
Hydrogen
invariant vectors
Invariants
Magnetic fields
Mathematical models
Orbits
Quantum dots
Quantum physics
Redmond invariant
supergeneralized Runge–Lenz vector
Symmetry
France
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Summary:In this non-exhaustive review, we discuss the importance of invariant vectors in atomic physics, such as the Laplace–Runge–Lenz vector, the Redmond vector in the presence of an electric field, the Landau–Avron–Sivardièrevector when the system is subject to a magnetic field, and the supergeneralized Runge–Lenz vector for the two-center problem. The application to the Stark and Zeeman effects are outlined. The existence of constants of motion in the charge-dyon system is also briefly mentioned.
Bibliography:ObjectType-Article-1
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ISSN:2218-2004
2218-2004
DOI:10.3390/atoms11070105