scholarly journals Lower bounds of the gap between the first and second eigenvalues of the Schrödinger operator

1986 ◽  
Vol 294 (1) ◽  
pp. 341-341 ◽  
Author(s):  
Qi Huang Yu ◽  
Jia Qing Zhong
Keyword(s):  
Lower Bounds ◽  
Schrödinger Operator ◽  
Schrodinger Operator

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.

On the trace of the difference of Schrödinger heat semigroups

1991 ◽  
Vol 119 (1-2) ◽  
pp. 169-175 ◽  
Author(s):  
M. van den Berg
Keyword(s):  
Laplace Operator ◽  
Lower Bounds ◽  
Schrödinger Operator ◽  
Compact Support ◽  
Upper And Lower Bounds ◽  
Schrodinger Operator ◽  
Heat Semigroups ◽  
The Difference ◽  
The Laplace Operator ◽  
Borel Measurable

SynopsisWe obtain upper and lower bounds for tr (e−th−etΔ), where H = −Δ + V is a Schrödinger operator on L2 (ℝm), and ℝ is the Laplace operator for ℝm. The bounds are obtained for a class of negative valued Borel measurable potentials with compact support and in L∞(ℝm).

scholarly journals On the two-dimensional Schrödinger operator with an attractive potential of the Bessel-Macdonald type

2020 ◽  
pp. 168385
Author(s):  
Wellisson B. De Lima ◽  
Oswaldo M. Del Cima ◽  
Daniel H.T. Franco ◽  
Bruno C. Neves
Keyword(s):  
Schrödinger Operator ◽  
Attractive Potential ◽  
Two Dimensional ◽  
Schrodinger Operator
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