Asymptotic behavior of the discrete spectrum of the Schrödinger operator in electric and homogeneous magnetic fields

1992 ◽  
Vol 62 (3) ◽  
pp. 2807-2814 ◽  
Author(s):  
A. V. Sobolev
Keyword(s):  
Asymptotic Behavior ◽  
Magnetic Fields ◽  
Discrete Spectrum ◽  
Schrödinger Operator ◽  
Schrodinger Operator

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

1997 ◽  
Vol 145 ◽  
pp. 29-68 ◽  
Author(s):  
Tetsuya Hattori
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Discrete Spectrum ◽  
Schrödinger Operator ◽  
Atomic System ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Many Body

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)

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