Abstract
The upper bound for the asymptotic behavior of the coefficients of expansion of the evolution operator kernel in powers of the time intervalΔt was obtained. It was found that for nonpolynomial potentials, the coefficients may increase as n!. But this increase may be slower if contributions with opposite signs cancel each other. In particular, an example of the potential for which the expansion converges is presented. For polynomial potentials, theΔt-expansion is clearly the asymptotic one. In this case, the coefficients increase asΓ(n L−2/L+2), where L is the order of the polynomial.
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