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Discrete spectrum of many body Schrödinger operators with non-constant magnetic fields I

Published online by Cambridge University Press:  22 January 2016

Tetsuya Hattori
Tetsuya Hattori*
Affiliation:
Department of Mathematics, Faculty of Science Osaka University, Toyonaka, Osaka 560, Japan
*
Department of Mechanics and Applied MathematicsOsaka Institute of Technology, 5-16-1, Omiya, Asahi-ku, Osaka 535, Japan
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In this paper we discuss the discrete spectrum of the Schrödinger operator HNZ(b), defined as below, for an atomic system in a magnetic field. Let where xj is a point in R3 (1 ≥ j ≥ N), and ∇j be the gradient in R3 with respect to xj (1 ≥ j ≥ N). Then we consider the following operator:

(1.1)

defined on , where 3 being real-valued and

(1.2)

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 145 , March 1997 , pp. 29 - 68
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

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