Abstract
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.
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Slobodenyuk, V.A. Investigation of the Kernel of the Evolution Operator for One Class of Potentials. Russian Physics Journal 43, 944–951 (2000). https://doi.org/10.1023/A:1011383009146
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DOI: https://doi.org/10.1023/A:1011383009146