# Eigenvalue estimates for the one-particle density matrix

@article{Sobolev2022EigenvalueEF,
title={Eigenvalue estimates for the one-particle density matrix},
author={Alexander V. Sobolev},
journal={Journal of Spectral Theory},
year={2022}
}
• A. Sobolev
• Published 25 August 2020
• Mathematics
• Journal of Spectral Theory
It is shown that the eigenvalues $\lambda_k, k=1, 2, \dots,$ of the one-particle density matrix satisfy the bound $\lambda_k\le C k^{-8/3}$ with a positive constant $C$.
3 Citations

### Eigenvalue asymptotics for the one-particle density matrix

describing an atom withN particles (e.g. electrons) with coordinates x = (x1, x2, . . . , xN ), xk ∈ R, k = 1, 2, . . . , N , and a nucleus with charge Z > 0. The notation ∆k is used for the

• 2022

## References

SHOWING 1-10 OF 18 REFERENCES

### Eigenvalue asymptotics for the one-particle density matrix

describing an atom withN particles (e.g. electrons) with coordinates x = (x1, x2, . . . , xN ), xk ∈ R, k = 1, 2, . . . , N , and a nucleus with charge Z > 0. The notation ∆k is used for the

### Exponential bounds and absence of positive eigenvalues forN-body Schrödinger operators

• Mathematics
• 1982
For a large class ofN-body potentialsV we prove that if ϕ is an eigenfunction of −δ+V with eigenvalueE then sup{α2+E:α≧0, exp(α|x|)ϕ∈L2} is either a threshold or +∞. Consequences of this result are

### Estimates on derivatives of Coulombic wave functions and their electron densities

• Mathematics
Journal für die reine und angewandte Mathematik
• 2021
Abstract We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions ψ, involving negative powers of the distance to the singularities of the many-body potential. We use

### Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators

• Mathematics
• 1973
O'Connor's approach to spatial exponential decay of eigenfunctions for multiparticle Schrödinger Hamiltonians is developed from the point of view of analytic perturbations with respect to

### Sharp Regularity Results for Coulombic Many-Electron Wave Functions

• Mathematics
• 2003
We show that electronic wave functions ψ of atoms and molecules have a representation ψ=ϕ, where is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution

### Analytic Structure of Many-Body Coulombic Wave Functions

• Mathematics
• 2009
We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with {{\bf x} =

### Local properties of Coulombic wave functions

• Mathematics
• 1994
We investigate the local behaviour of solutions of a nonrelativistic Schrödinger equation which describe Coulombic systems. Firstly we give a representation theorem for such solutions in the

### An Interesting Class of Operators with unusual Schatten-von Neumann behavior

• Mathematics
• 2001
We consider the class of integral operators Q' on L 2 (R+) of the form (Q'f)(x) = R 1 0 '(max{x,y})f(y)dy. We discuss necessary and sucient conditions on ' to insure that Q' is bounded, compact, or

### Pointwise bounds on eigenfunctions and wave packets inN-body quantum systems IV

• Mathematics
• 1978
AbstractWe describe several new techniques for obtaining detailed information on the exponential falloff of discrete eigenfunctions ofN-body Schrödinger operators. An example of a new result is the

### ESTIMATES OF SINGULAR NUMBERS OF INTEGRAL OPERATORS

• Mathematics
• 1977
ContentsIntroduction § 1. Operator spaces and function spaces § 2. Estimates of singular numbers based on the method of piecewise-polynomial approximation § 3. Interpolation methods § 4. General