On the Constructively Determination the Spectral Invariants of the Periodic Multidimensional Schrodinger Operator

TL;DR

This paper presents a constructive method to determine spectral invariants of multidimensional Schrödinger operators with periodic potentials using band functions, advancing spectral analysis techniques.

Contribution

It introduces a novel constructive approach to identify spectral invariants from band functions in multidimensional periodic Schrödinger operators.

Findings

Spectral invariants can be explicitly constructed from band functions.

The method applies to multidimensional Schrödinger operators with periodic potentials.

Provides a new tool for spectral analysis in quantum mechanics.

Abstract

In this paper we constructively determine a family of the spectral invariants of the multidimensional Schrodinger operator with a periodic potential by the given band functions.