A Rellich Type Theorem for The Generalized Oscillator

IF 1.2 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Reports on Mathematical Physics Pub Date : 2025-06-01 DOI:10.1016/S0034-4877(25)00029-1

Tomoya Tagawa

引用次数: 0

Abstract

For the Schrödinger operator generalized from the harmonic oscillator, we prove a Rellich type theorem, which characterizes the order of growth of eigenfunctions at infinity. The proofs are given by an extensive use of commutator arguments invented recently by Ito and Skibsted. These arguments are simple and elementary and do not employ energy cut-offs or microlocal analysis.

查看原文本刊更多论文

广义振子的一个Rellich型定理

对于由谐振子推广而来的Schrödinger算子，我们证明了一个表征特征函数在无穷远处生长的阶数的Rellich型定理。这些证明是通过广泛使用伊藤和斯基斯特特德最近发明的换向子论证给出的。这些论点是简单和基本的，没有使用能量切断或微局部分析。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Reports on Mathematical Physics 物理-物理：数学物理

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Reports on Mathematical Physics publish papers in theoretical physics which present a rigorous mathematical approach to problems of quantum and classical mechanics and field theories, relativity and gravitation, statistical physics, thermodynamics, mathematical foundations of physical theories, etc. Preferred are papers using modern methods of functional analysis, probability theory, differential geometry, algebra and mathematical logic. Papers without direct connection with physics will not be accepted. Manuscripts should be concise, but possibly complete in presentation and discussion, to be comprehensible not only for mathematicians, but also for mathematically oriented theoretical physicists. All papers should describe original work and be written in English.