The quantum mechanical virial theorem and the absence of positive energy bound states of Schrödinger operators

1975 ◽  
Vol 20 (1) ◽  
pp. 57-69 ◽  
Author(s):  
Hubert Kalf
Keyword(s):  
Bound States ◽  
Virial Theorem ◽  
Schrödinger Operators ◽  
Positive Energy ◽  
Quantum Mechanical ◽  
Schrodinger Operators ◽  
Energy Bound

Non-existence of eigenvalues of Schrödinger operators

1977 ◽  
Vol 79 (1-2) ◽  
pp. 157-172 ◽  
Author(s):  
H. Kalf
Keyword(s):  
Schrödinger Operator ◽  
Exterior Domain ◽  
Virial Theorem ◽  
Schrödinger Operators ◽  
Quantum Mechanical ◽  
Schrodinger Operators ◽  
Schrodinger Operator ◽  
Image Position

SynopsisThe paper provides conditions which enstlre that the Schrödinger operatordefined on an exterior domain has no eigenvalues on a certain half-ray. These conditions are in terms of weak local assumptions onThe proof uses Kato's ideas [16] in conjunction with the physicists' “commutator proof” of the quantum mechanical virial theorem.

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.

scholarly journals Number of Bound States of Schrödinger Operators with Matrix-Valued Potentials

2007 ◽  
Vol 82 (2-3) ◽  
pp. 107-116 ◽  
Author(s):  
Rupert L. Frank ◽  
Elliott H. Lieb ◽  
Robert Seiringer
Keyword(s):  
Bound States ◽  
Schrödinger Operators ◽  
Schrodinger Operators
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