一维薛定谔方程的显式求解

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-01 DOI:10.1137/22m1514441

Peter C. Gibson

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引用次数: 0

摘要

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4466-4493 页，2024 年 8 月。摘要。对在李群 SU(1,1) 中取值的乘积积分进行求值，得到薛定谔方程阻抗形式的显式解。因此得到了具有任意紧凑支撑势的经典一维薛定谔算子的传输系数和[math]矩阵的显式公式。这些公式涉及标准双曲函数的算子理论类似物，为分析一维声学和量子散射提供了新工具。

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Explicit Solution of the 1D Schrödinger Equation

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4466-4493, August 2024.
Abstract. Evaluation of a product integral with values in the Lie group SU(1,1) yields the explicit solution to the impedance form of the Schrödinger equation. Explicit formulas for the transmission coefficient and [math]-matrix of the classical one-dimensional Schrödinger 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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来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.