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

Abstract

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)