Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling

1984/07/01 by Barry Simon · 4 citations
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum chaos and dynamical systems #Quantum Mechanics and Non-Hermitian Physics

paper · doi:10.2307/2007072

openalex publication_date 1984/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/17

Abstract

We discuss the leading asymptotics of eigenvalue splittings of - 2 + X2V in the limit as X -- o, and where V is a non-negative potential with several zeros. For example, if EO(X), E1(X) are the two lowest eigenvalues in -a situation where V has precisely two zeros, a and b, related by a symmetry, then limx . - (X)-lIn[E1(X) - EO(X)] is given as the distance from a to b in a certain Riemann metric.

Citations

• A class of analytic perturbations for one-body Schrödinger Hamiltonians
• Logarithmic Sobolev Inequalities

Cited by

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• Chaos and Quantum Tunneling
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• Barry Simon [wikipedia]