Spectral Analysis of N-Body Schrodinger Operators

1981/11/01 by Peter Perry, Israel Michael Sigal, Barry Simon · 4 citations
Mathematics · Physics and Astronomy · #Spectral Theory in Mathematical Physics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems

paper · doi:10.2307/1971301

openalex publication_date 1981/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

For a large class of two body potentials, we solve two of the main problems in the spectral analysis of multiparticle quantum Hamiltonians: explicitly, we prove that the point spectrum lies in a closed countable set (and describe that set in terms of the eigenvalues of Hamiltonians of subsystems) and that there is no singular continuous spectrum. We accomplish this by extending Mourre's work on three body problems to N-body problems.

Cited by

• Commutator methods for the spectral analysis of uniquely ergodic dynamical systems
• Limiting Absorption Principle for Discrete Schrödinger Operators with a Wigner–von Neumann Potential and a Slowly Decaying Potential
• Tosio Kato's Work on Non--Relativistic Quantum Mechanics
• Barry Simon [wikipedia]