Spectral Asymptotics for Magnetic Schroedinger Operator

TL;DR

This paper derives eigenvalue asymptotics for various magnetic quantum operators in 2D and 3D, highlighting differences due to dimensionality and operator type, which are crucial for understanding magnetic effects in quantum systems.

Contribution

It provides new eigenvalue asymptotics for 2D and 3D magnetic Schrödinger, Schrödinger-Pauli, and Dirac operators, emphasizing the impact of magnetic fields and dimensionality.

Findings

Eigenvalue asymptotics established for 2D and 3D operators.

Significant differences identified between 2D and 3D cases.

Results enhance understanding of magnetic effects in quantum operators.

Abstract

In this article we obtain eigenvalue asymptotics for 2D and 3D-Schroedinger, Schroedinger-Pauli and Dirac operators in the situations in which the role of the magnetic field is important. These operators are essentially different and there is a significant difference between 2D and 3D-operators.