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Coulomb Potentials by Path Integration
Author(s) -
Grosche C.
Publication year - 1992
Publication title -
fortschritte der physik/progress of physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.2190400802
Subject(s) - parabolic coordinates , log polar coordinates , bipolar coordinates , orthogonal coordinates , prolate spheroidal coordinates , action angle coordinates , cartesian coordinate system , generalized coordinates , polar coordinate system , physics , electric potential , coulomb , elliptic coordinate system , spherical coordinate system , path integral formulation , coulomb wave function , classical mechanics , quantum mechanics , mathematics , geometry , electron , voltage , quantum
The path integral for the potentialis evaluated in three different coordinate systems, i. e. in cartesian coordinates, in polar coordinates and in parabolic coordinates. The equivalence between the different approaches is shown and in each case the energyspectrum and the wave functions are explicitly calculated. Furthermore we discuss special cases, including the ring‐potential, the Coulomb potential with an Aharonov‐Bohm solenoid, and the genuine Coulomb problem. We also point out the separability of the path integral formulation of the ring‐potential in spheroidal coordinates, and of the Coulomb potential in spheroidal and spheroconical coordinates, respectively.