Expressions of the Green function in terms of reflection coefficients
Toru Miyazawa
TL;DR
This paper derives exact expressions for the Green function of the one-dimensional Schrödinger equation using reflection coefficients, connecting these results to the WKB approximation.
Contribution
It introduces a novel formulation expressing the Green function explicitly through reflection coefficients for semi-infinite intervals.
Findings
Exact Green function expressions in terms of reflection coefficients
Connection established between these expressions and the WKB approximation
Provides a new perspective on solving the Schrödinger equation
Abstract
We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and the WKB approximation.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics