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WKB expansions with higher order corrections: The general case

Florentin Langouche, D. Roekaerts, E. Tirapegui

Physics Letters AAug 1, 19798 citations

Time-dependent WKB expansion for the non-relativistic coulomb propagator

S. M. Blinder

Chemical Physics LettersFeb 1, 19873 citations

WKB Wave Function of the General Time-Dependent Quadratic Hamiltonian System

Jeong Ryeol Choi

International Journal of Theoretical PhysicsApr 1, 20042 citations

WKB Approximation in Quantum Mechanics

Boris Mikhailovich Karnakov, В. П. Крайнов

Springer eBooksAug 28, 20121 citation

The General Expansion of WKB Approximation method to the Propagator for Arbitrary Hamiltonians

Zhiqiang Hu

The general method of path integrals in quantum mechanics introduced by R.P.Feynman is applied in this paper to discuss the amplitude of transition probability in quantum mechanics, that is, the subject of the propagator.Mauriel M.Mizrahi's semiclassical (WKB) approximation method has been used in studying the general expansion in detail for the propagator corresponding to an arbitrary Hamiltonian operator H. ?? where S_c is the action functional evaluated at the classical path (q_c, p_c) , ρ is a constant, ?? Maurice M.Mizrahi's solution of the K_(WKB) expansion has been generalized, and another linear independent particular solution is obtained.This is the solution when 0~2 = det M equals zero.The K_(WKB) can be applied to all systems corresponding to an arbitrary Hamiltonian operator.The general method of path integrals in quantum mechanics introduced by R.P.Feynman is applied in this paper to discuss the amplitude of transition probability in quantum mechanics, that is, the subject of the propagator.Mauriel M.Mizrahi's semiclassical (WKB) approximation method has been used in studying the general expansion in detail for the propagator corresponding to an arbitrary Hamiltonian operator H. ?? where S_c is the action functional evaluated at the classical path (q_c, p_c) , ρ is a constant, ?? Maurice M.Mizrahi's solution of the K_(WKB) expansion has been generalized, and another linear independent particular solution is obtained.This is the solution when 0~2 = det M equals zero.The K_(WKB) can be applied to all systems corresponding to an arbitrary Hamiltonian operator.

Huadong Shifan Daxue xuebao. Ziran kexue banJan 1, 19830 citations

Phase space path integrals, without limiting procedure

Maurice M. Mizrahi

This paper defines path integrals in phase space without using a time-division approach followed by a limiting process, thereby generalizing a similar procedure used in configuration space. This is useful since the path integral approach cannot always be formulated in configuration space (e.g., when the Hamiltonian is arbitrary) but can always be formulated in phase space. The most general Gaussian measure, absorbing the quadratic portion of the functional to be integrated, is constructed, and large classes of path integrals are evaluated with respect to it. Applications are given to the perturbation expansion and the semiclassical (WKB) expansion for arbitrary Hamiltonians.This paper defines path integrals in phase space without using a time-division approach followed by a limiting process, thereby generalizing a similar procedure used in configuration space. This is useful since the path integral approach cannot always be formulated in configuration space (e.g., when the Hamiltonian is arbitrary) but can always be formulated in phase space. The most general Gaussian measure, absorbing the quadratic portion of the functional to be integrated, is constructed, and large classes of path integrals are evaluated with respect to it. Applications are given to the perturbation expansion and the semiclassical (WKB) expansion for arbitrary Hamiltonians.

Journal of Mathematical PhysicsJan 1, 197854 citations

WKB Expansion for arbitrary Hamiltonians

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