Exact path integral of the hydrogen atom and the Jacobi's principle of least action
Abstract
The general treatment of a separable Hamiltonian of Liouvilletype is wellknown in operator formalism. A path integral counterpart is formulated if one starts with the Jacobi's principle of least action, and a path integral evaluation of the Green's function for the hydrogen atom by Duru and Kleinert is recognized as a special case. The Jacobi's principle of least action for given energy is reparametrization invariant, and the separation of variables in operator formalism corresponds to a choice of gauge in path integral. The Green's function is shown to be gauge independent,if the operator ordering is properly taken into account. These properties are illustrated by evaluating an exact path integral of the Green's function for the hydrogen atom in parabolic coordinates.
 Publication:

arXiv eprints
 Pub Date:
 August 1996
 DOI:
 10.48550/arXiv.hepth/9608052
 arXiv:
 arXiv:hepth/9608052
 Bibcode:
 1996hep.th....8052F
 Keywords:

 High Energy Physics  Theory
 EPrint:
 10 pages. Talk presented at Inauguration Conference of Asia Pacific Center for Theoretical Physics, Seoul, Korea, June 410,1996 (To be published in the Proceedings(World Scientific, Singapore))