Spectrum of semiclassical Schrödinger operators for two-frequency resonance

2021 ◽  
pp. 1-10
Author(s):  
Faouzi Hireche ◽  
Kaoutar Ghomari
Keyword(s):  
Normal Form ◽  
Discrete Spectrum ◽  
Global Minimum ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Frequency Resonance

This article is devoted to an analysis of semiclassical Schrödinger operators for two-frequency resonance of the type 1 : p where p is even. The Birkhoff–Gustavson normal form is applied to describe the discrete spectrum in the case where the potential is smooth and admits a nondegenerate global minimum at the origin 0.

Localization of Discrete Spectrum of Multiparticle Schrödinger Operators

1985 ◽  
Vol 40 (10) ◽  
pp. 1052-1058 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Discrete Spectrum ◽  
Lower Bounds ◽  
Upper Bound ◽  
Schrödinger Operators ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators

An upper bound on the dimension of eigenspaces of multiparticle Schrödinger operators is given. Its relation to upper and lower bounds on the eigenvalues is discussed.

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

1997 ◽  
Vol 145 ◽  
pp. 69-98
Author(s):  
Tetsuya Hattori
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Discrete Spectrum ◽  
Bound States ◽  
Atomic System ◽  
Energy Levels ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Many Body ◽  
Discrete Energy

This paper is continuation from [10], in which we studied the discrete spectrum of atomic Hamiltonians with non-constant magnetic fields and, more precisely, we showed that any atomic system has only finitely many bound states, corresponding to the discrete energy levels, in a suitable magnetic field. In this paper we show another phenomenon in non-constant magnetic fields that any atomic system has infinitely many bound states in a suitable magnetic field.

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