The asymptotic distribution of discrete eigenvalues for Schr\"odinger operators

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

On Positive Eigenvalues of One - Body Schrodinger Operators

The last twenty years have produced a rather extensive literature on the exact mathematical treatment of general features of the Schrodinger equation for one or many particles. One of the more intriguing questions concerns the presence of discrete eigenvalues of positive energy (that is square-integrable eigenfunctions with positive eigenvalues) . There is a highly non-rigorous but physically a...

Asymptotic Distribution of Eigenvalues for Pauli Operators with Nonconstant Magnetic Fields

Asymptotic Distribution of Eigenvalues for Some Elliptic Operators with Simple Remainder Estimates

We are interested in remainder estimates in the Weyl formula for the asymptotic number of eigenvalues of certain elliptic operators on R and on a smooth compact manifold without boundary. The main aim of this paper is to compare spectral asymptotics of operators with irregular coefficients and certain classes of smoothed operators for which the Weyl formula is derived by means of elementary pse...

Asymptotic distribution of negative eigenvalues for two dimensional Pauli operators with nonconstant magnetic fields