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- Title
Stationary Schrödinger equation in nonrelativistic quantum mechanics and the functional integral.
- Authors
Efimov, G.
- Abstract
We formulate a method for representing solutions of homogeneous second-order equations in the form of a functional integral or path integral. As an example, we derive solutions of second-order equations with constant coefficients and a linear potential. The method can be used to find general solutions of the stationary Schrödinger equation. We show how to find the spectrum and eigenfunctions of the quantum oscillator equation. We obtain a solution of the stationary Schrödinger equation in the semiclassical approximation, without a singularity at the turning point. In that approximation, we find the coefficient of transmission through a potential barrier. We obtain a representation for the elastic potential scattering amplitude in the form of a functional integral.
- Subjects
SCHRODINGER equation; NONRELATIVISTIC quantum mechanics; FUNCTIONAL analysis; INTEGRALS; PATH integrals; EIGENFUNCTIONS; SCATTERING amplitude (Physics); APPROXIMATION theory
- Publication
Theoretical & Mathematical Physics, 2012, Vol 171, Issue 3, p812
- ISSN
0040-5779
- Publication type
Article
- DOI
10.1007/s11232-012-0077-7