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On the Dirac–Kepler problem: The Johnson–Lippmann operator, supersymmetry, and normal‐mode representations
Author(s) -
Dahl Jens Peder,
Jøorgensen Thomas
Publication year - 1995
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560530204
Subject(s) - kepler , dirac (video compression format) , dirac operator , supersymmetry , theoretical physics , mathematical physics , physics , operator (biology) , kepler problem , mode (computer interface) , quantum mechanics , classical mechanics , astronomy , computer science , chemistry , stars , biochemistry , repressor , transcription factor , neutrino , gene , operating system
The relativistic Kepler problem is discussed, with emphasis on the exact supersymmetry of the problem. It is shown that the supersymmetry is generated by the Johnson–Lippmann operator. Two related operators are found to generate new supersymmetries in an extended function space. Each of these supersymmetries may be disguised as radial supersymmetries. The radial supersymmetries are discussed and it is shown that each of them defines a normal‐mode representation of the hydrogen‐atom radial functions. Thus, one obtains two different, but equivalent, analytical expressions for these functions. The expressions are well known, but are rederived here in the light of the new understanding. Finally, the nonrelativistic image of the relativistic supersymmetry is constructed and its generators shown to be identical with those recently presented in the literature. © 1995 John Wiley & Sons, Inc.