Convergence of the Schwinger  DeWitt Expansion for Some Potentials
Abstract
It is studied time dependence of the evolution operator kernel for the Schrödinger equation with a help of the Schwinger  DeWitt expansion. For many of potentials this expansion is divergent. But there were established nontrivial potentials for which the Schwinger  DeWitt expansion is convergent. These are, e.g., V=g/x^2, V=g/cosh^2 x, V=g/sinh^2 x, V=g/sin^2 x. For all of them the expansion is convergent when $g=\lambda (\lambda 1)/2$ and $\lambda$ is integer. The theories with these potentials have no divergences and in this meaning they are "good" potentials contrary to other ones. So, it seems natural to pay special attention namely to these "good" potentials. Besides convergence they have other interesting feature: convergence takes place only for discrete values of the charge $g$. Hence, in the theories of this class the charge is quantized.
 Publication:

arXiv eprints
 Pub Date:
 March 1997
 DOI:
 10.48550/arXiv.hepth/9703169
 arXiv:
 arXiv:hepth/9703169
 Bibcode:
 1997hep.th....3169S
 Keywords:

 High Energy Physics  Theory
 EPrint:
 9 pages, LaTeXfile, to be published in Int. Jour. of Theor. Phys. as Proc. of Conf. "Quantum Structures' 96, Berlin"