Scholarlink

Abstract <p> We describe semiclassical spectral series of the one-dimensional Schrödinger operator with a potential having a smoothed jump whose width tends to zero more slowly than the semiclassical parameter. We calculate asymptotic eigenvalues from the quantization conditions of a one-dimensional bundle over a circle constructed from the classical Hamiltonian, and describe the asymptotic behavior of eigenfunctions using a modification of Maslov’s canonical operator on this bundle. </p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quantization Conditions for a Bundle over a Circle and Semiclassical Spectral Series of the One-Dimensional Schrödinger Operator with a Jump-like Two-Scale Potential

  • 期刊论文

  • 发表日期：

    2025年9月1日

查看全文
  • I. A. Lavrinenko,
  • A. I. Shafarevich

摘要

Abstract

We describe semiclassical spectral series of the one-dimensional Schrödinger operator with a potential having a smoothed jump whose width tends to zero more slowly than the semiclassical parameter. We calculate asymptotic eigenvalues from the quantization conditions of a one-dimensional bundle over a circle constructed from the classical Hamiltonian, and describe the asymptotic behavior of eigenfunctions using a modification of Maslov’s canonical operator on this bundle.