Abstract. Cwikel's bound is extended to an operator-valued setting. One application of this result is a semi-classical bound for the number of negative bound states for Schrodinger operators with operator-valued potentials. We recover Cwikel's bound for the Lieb--Thirring constant L0;3 which is far worse than the best available by Lieb (for scalar potentials). However, it leads to a uniform bound (in the dimension d 3) for the quotient L0;d =L cl
|
130
|
Methods of Modern Mathematical Physics IV: Analysis of Operators
– Reed, Simon
- 1978
|
|
103
|
Introduction to the theory of linear nonselfadjoint operators
– Gohberg, Krein
- 1969
|
|
77
|
Methods of Modern Mathematical Physics I: Functional Analysis
– Reed, Simon
- 1980
|
|
52
|
Inequalities for the moments of the eigenvalues of the Schrodinger Hamiltonian and their relation to Sobolev inequalities
– Lieb, Thirring
- 1976
|
|
41
|
Functional integration and quantum physics
– Simon
- 1979
|
|
36
|
Thomas--Fermi and related theories of atoms and molecules
– Lieb
- 1981
|
|
29
|
Spectral theory of self-adjoint operators in Hilbert space
– Birman, Z
- 1987
|
|
28
|
Weak type estimates for singular values and the number of bound states of Schrodinger operators
– Cwikel
- 1977
|
|
26
|
Quantum Mechanics for Hamiltonians Defined as Quadratic Forms
– Simon
- 1971
|
|
22
|
On the Schrodinger equation and the eigenvalue problem
– Li, Yau
- 1983
|
|
22
|
Bound for the kinetic energy of fermions which proves the stability of matter, Phys
– Lieb, Thirring
- 1975
|
|
19
|
A sharp bound for an eigenvalue moment of the one-dimensional Schrodinger operator
– Hundertmark, Lieb, et al.
- 1998
|
|
18
|
Distribution of the discrete spectrum of singular differential operators
– Rozenblum
- 1972
|
|
17
|
Sharp Lieb-Thirring inequalities in high dimensions
– Laptev, Weidl
- 2000
|
|
15
|
The spectrum of singular boundary problems
– Birman
- 1961
|
|
15
|
On the bound states of a given potential
– Schwinger
- 1961
|
|
13
|
Bounds on the eigenvalues of the Laplace and Schrodinger operators
– Lieb
- 1976
|
|
12
|
On semi-classical bounds for eigenvalues of Schrödinger operators
– Aizenman, Lieb
- 1978
|
|
12
|
New bounds on the Lieb-Thirring constants
– Hundertmark, Laptev, et al.
- 2000
|
|
11
|
D.: Riesz means of bounded states and semi-classical limit connected with a Lieb-Thirring conjecture I,II
– Helffer, Robert
- 1990
|
|
5
|
A new proof of the Cwikel-Lieb-Rosenbljum bound
– Conlon
- 1985
|
|
5
|
A family of optimal conditions for the absence of bound states in a potential
– Glaser, Grosse, et al.
- 1976
|
|
5
|
Dirichlet and Neumann eigenvalue problems on domains in Euclidian spaces
– Laptev
- 1997
|
|
5
|
On the Lieb-Thirring constants L fl;1 for fl 1=2
– Weidl
- 1996
|
|
3
|
Recent results on Lieb-Thirring inequalities
– Laptev, Weidl
- 2000
|
|
1
|
On a theorem of Laptev and Weidl
– Benguria, Loss
- 2000
|
|
1
|
Private communication
– Laptev
|
|
1
|
states of two-body Schrodinger operators -- A review
– Simon, Bound
- 1976
|
|
1
|
On the Lieb-Thirring constants L #,1 for # # 1/2
– Weidl
- 1996
|
|
