Lower Bounds for Shape Resonances Widths of Schrödinger Operators

2001 ◽  
pp. 247-257 ◽  
Author(s):  
Nicolas Burq
Keyword(s):  
Lower Bounds ◽  
Schrödinger Operators ◽  
Schrodinger Operators ◽  
Shape Resonances

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 Spectral Analysis of Schrödinger Operators with Unusual Semiclassical Behavior

10.14311/1801 ◽  
2013 ◽  
Vol 53 (3) ◽  
Author(s):  
Pavel Exner ◽  
Diana Barseghyan
Keyword(s):  
Spectral Analysis ◽  
Phase Space ◽  
Lower Bounds ◽  
Dirichlet Boundary ◽  
Schrödinger Operators ◽  
Critical Value ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Two Dimensional ◽  
Eigenvalue Bounds

In this paper we discuss several examples of Schrödinger operators describing a particle confined to a region with thin cusp-shaped ‘channels’, given either by a potential or by a Dirichlet boundary; we focus on cases when the allowed phase space is infinite but the operator still has a discrete spectrum. First we analyze two-dimensional operators with the potential |xy|p - ?(x2 + y2)p/(p+2)where p?1 and ??0. We show that there is a critical value of ? such that the spectrum for ??crit it is unbounded from below. In the subcriticalcase we prove upper and lower bounds for the eigenvalue sums. The second part of work is devoted toestimates of eigenvalue moments for Dirichlet Laplacians and Schrödinger operators in regions havinginfinite cusps which are geometrically nontrivial being either curved or twisted; we are going to showhow these geometric properties enter the eigenvalue bounds.

Localization of Eigenvalues by a Modification of Müller′s Variational Principle in Some Exactly Solvable Cases

1983 ◽  
Vol 38 (5) ◽  
pp. 493-496 ◽  
Author(s):  
Heinz K. H. Siedentop
Keyword(s):  
Variational Principle ◽  
Lower Bounds ◽  
Schrödinger Operators ◽  
Three Dimensional ◽  
Finite Depth ◽  
Upper And Lower Bounds ◽  
Schrodinger Operators ◽  
Potential Well ◽  
Rough Approximation ◽  
Exactly Solvable

Upper and lower bounds on the eigenvalues of Schrödinger operators with simple one and a simple three dimensional potential (well of finite depth, spherical δ-potential) are given by means of a modification of Müller′s variational principle. The estimates, comparing them with the exact eigenvalues, show a localization of the eigenvalues even in a rough approximation for the trial operator.

scholarly journals Lower bounds for Schrödinger operators in H¹(ℝ)

1999 ◽  
Vol 132 (1) ◽  
pp. 79-89
Author(s):  
Ronan Pouliquen
Keyword(s):  
Lower Bounds ◽  
Schrödinger Operators ◽  
Schrodinger Operators
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