EXPLICIT SOLUTION OF THE 1D SCHRODINGER EQUATION

被引：0
|
作者：
Gibson, Peter C. [1 ]
机构：
[1] York Univ, Dept Math & Stat, Toronto, ON M3J 1P3, Canada
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2024年 / 56卷 / 04期
关键词：
one-dimensional Schrodinger equation; one-dimensional wave equation; explicit solutions; scattering on the line; INVERSE SPECTRAL THEORY; STURM-LIOUVILLE OPERATORS; SCATTERING;
D O I：
10.1137/22M1514441
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Evaluation of a product integral with values in the Lie group SU(1,1) yields the explicit solution to the impedance form of the Schro"\dinger equation. Explicit formulas for the transmission coefficient and S-matrix of the classical one-dimensional Schro"\dinger operator with arbitrary compactly supported potential are obtained as a consequence. The formulas involve operator theoretic analogues of the standard hyperbolic functions and provide new tools with which to analyze acoustic and quantum scattering in one dimension.
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页码：4466 / 4493
页数：28
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