caa a22 4500 475822870 CHVBK 20180406123823.0 cr unu---uuuuu 170329e20001101xx s 000 0 eng 10.1023/A:1011383009146 doi (NATIONALLICENCE)springer-10.1023/A:1011383009146 Slobodenyuk V. Ulyanovsk State University, Russia aut Investigation of the Kernel of the Evolution Operator for One Class of Potentials [Elektronische Daten] [V. Slobodenyuk] The convergence of the Schwinger-DeWitt expansion in quantum mechanics is investigated for a special class of potentials for which the squared derivative of a potential (e.g., the centrifugal potential, the modified Peschle-Teller potential, or the potential specified by the Weierstrass function) is represented as a polynomial in the powers of the potential itself. It has been established for which representatives of the class the expansion diverges and for which it converges (convergence may take place only at certain discrete values of the charge). For potentials singular at zero, the absence of singularities in the formula for the kernel has been demonstrated. A generalization of potentials with a converging expansion to a multidimensional case is proposed. Plenum Publishing Corporation, 2000 Russian Physics Journal Kluwer Academic Publishers-Plenum Publishers 43/11(2000-11-01), 944-951 1064-8887 43:11<944 2000 43 11182 https://doi.org/10.1023/A:1011383009146 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1023/A:1011383009146 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Slobodenyuk V. Ulyanovsk State University, Russia aut NATIONALLICENCE 773 0- Russian Physics Journal Kluwer Academic Publishers-Plenum Publishers 43/11(2000-11-01), 944-951 1064-8887 43:11<944 2000 43 11182 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer