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Regularization of the WKB integrals. (English) Zbl 1008.81024
Summary: A simple general method of regularization of the higher-order Wentzel-Kramers-Brillouin (WKB) integrals for the bound state problem of the one-dimensional Schrödinger equation with a real-analytic potential is proposed. The method is based upon the explicit separation of the integrand singularities. As an example, a contribution of the higher-order WKB corrections to the energy eigenvalues for the quasi-exactly solvable potential, V(x)=10x 2 +10x 4 +x 6 , is considered.
MSC:
81Q20Semi-classical techniques in quantum theory, including WKB and Maslov methods
81Q05Closed and approximate solutions to quantum-mechanical equations
81U15Exactly and quasi-solvable systems (quantum theory)