scholarly journals Discrete spectrum for Schrödinger operators with oscillating decaying potentials

2016 ◽  
Vol 438 (2) ◽  
pp. 551-564 ◽  
Author(s):  
Georgi Raikov
Keyword(s):  
Discrete Spectrum ◽  
Schrödinger Operators ◽  
Schrodinger Operators

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.

On the finiteness of the discrete spectrum of four-particle lattice Schrödinger operators

2003 ◽  
Vol 51 (1) ◽  
pp. 43-70 ◽  
Author(s):  
Sergio Albeverio ◽  
Saidakhmat N. Lakaev ◽  
Janikul I. Abdullaev
Keyword(s):  
Discrete Spectrum ◽  
Schrödinger Operators ◽  
Schrodinger Operators
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