Asymptotics of Wave Functions of the Stationary Schrödinger Equation in the Weyl Chamber

S. Yu Dobrokhotov, D. S. Minenkov, S. B. Shlosman

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We study stationary solutions of the Schrödinger equation with a monotonic potential U in a polyhedral angle (Weyl chamber) with the Dirichlet boundary condition. The potential has the form U(x)=∑j=1nV(xj),x=(x1,…,xn)∈ℝn, with a monotonically increasing function V (y). We construct semiclassical asymptotic formulas for eigenvalues and eigenfunctions in the form of the Slater determinant composed of Airy functions with arguments depending nonlinearly on xj. We propose a method for implementing the Maslov canonical operator in the form of the Airy function based on canonical transformations.

Original languageEnglish
Pages (from-to)1626-1634
Number of pages9
JournalTheoretical and Mathematical Physics
Volume197
Issue number2
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

  • Airy function
  • boundary value problem
  • Maslov canonical operator
  • quantization condition
  • spectrum
  • stationary Schrödinger equation
  • Weyl-chamber-type polyhedral angle

Fingerprint

Dive into the research topics of 'Asymptotics of Wave Functions of the Stationary Schrödinger Equation in the Weyl Chamber'. Together they form a unique fingerprint.

Cite this