Semiclassical analysis for Hamiltonian in the Born-Oppenheimer approximation

Authors

  • Senoussaoui Abderrahmane

DOI:

https://doi.org/10.11113/matematika.v30.n.705

Abstract

The purpose of this paper is to show that the operator H (h) = −h^2 × (delta)x − (delta)y + V (x, y) ,V is continuous (or V such that L^2 `Rnx × Rpy´), and V (x, y) approches infinity as ||x|| + ||y||approches infinity, has purely discrete spectrum. We give an application to the harmonic oscillator. Keywords: Discrete spectrum; harmonic oscillator; locally compact operator. 2010 Mathematics Subject Classification: 35J10, 35Q55

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Published

01-12-2014

Issue

Volume 30 (December 2014)

Section

Analysis and Algebra

License

Copyright of articles that appear in MATEMATIKA: MJIAM belongs exclusively to Penerbit UTM Press, Universiti Teknologi Malaysia. This copyright covers the rights to reproduce the article, including reprints, electronic reproductions or any other reproductions of similar nature.

How to Cite

Semiclassical analysis for Hamiltonian in the Born-Oppenheimer approximation. (2014). MATEMATIKA, 30, 135-144. https://doi.org/10.11113/matematika.v30.n.705