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• W1660621352 abstract "The Schwinger--DeWitt expansion for the evolution operator kernel is used to investigate analytical properties of the Schrodinger equation solution in time variable. It is shown, that this expansion, which is in general asymptotic, converges for a number of potentials (widely used, in particular, in one-dimensional many-body problems), and besides, the convergence takes place only for definite discrete values of the coupling constant. For other values of charge the divergent expansion determines the functions having essential singularity at origin (beyond usual $delta$-function). This does not permit one to fulfil the initial condition. So, the function obtained from the Schrodinger equation cannot be the evolution operator kernel. The latter, rigorously speaking, does not exist in this case. Thus, the kernel exists only for definite potentials, and moreover, at the considered examples the charge may have only quantized values." @default.
• W1660621352 created "2016-06-24" @default.
• W1660621352 creator A5007190760 @default.
• W1660621352 date "1995-06-19" @default.
• W1660621352 modified "2023-09-27" @default.
• W1660621352 title "Analytical Properties of Solutions of the Schrodinger Equation and Quantization of Charge" @default.
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