scholarly journals SCHRÖDINGER SECANT LOWER BOUNDS TO SEMIRELATIVISTIC EIGENVALUES

2007 ◽  
Vol 22 (10) ◽  
pp. 1899-1904 ◽  
Author(s):  
RICHARD L. HALL ◽  
WOLFGANG LUCHA
Keyword(s):  
Lower Bounds ◽  
Schrödinger Operator ◽  
Ground State ◽  
Schrodinger Operator ◽  
Bounded Below

It is shown that the ground-state eigenvalue of a semirelativistic Hamiltonian of the form [Formula: see text] is bounded below by the Schrödinger operator m + β p2 + V, for suitable β>0. An example is discussed.

scholarly journals Ground-state positivity, negativity, and compactness for a Schrödinger operator in RN

2007 ◽  
Vol 245 (1) ◽  
pp. 213-248 ◽  
Author(s):  
Bénédicte Alziary ◽  
Jacqueline Fleckinger-Pellé ◽  
Peter Takáč
Keyword(s):  
Schrödinger Operator ◽  
Ground State ◽  
Schrodinger Operator

scholarly journals Ground State for the Schrödinger Operator with the Weighted Hardy Potential

2011 ◽  
Vol 2011 ◽  
pp. 1-26
Author(s):  
J. Chabrowski ◽  
K. Tintarev
Keyword(s):  
Laplace Operator ◽  
Schrödinger Operator ◽  
Ground State ◽  
Ground States ◽  
Schrodinger Operator ◽  
Hardy Potential ◽  
Higher Integrability ◽  
Hardy Type ◽  
The Laplace Operator ◽  
Type Potential

We establish the existence of ground states on for the Laplace operator involving the Hardy-type potential. This gives rise to the existence of the principal eigenfunctions for the Laplace operator involving weighted Hardy potentials. We also obtain a higher integrability property for the principal eigenfunction. This is used to examine the behaviour of the principal eigenfunction around 0.

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