Heat Kernel Coefficients for Two-Dimensional Schrodinger Operators

TL;DR

This paper computes the Hadamard coefficients for two-dimensional integrable Schrödinger operators, advancing understanding of their mathematical properties and connections to Huygens' principle.

Contribution

It provides explicit calculations of heat kernel coefficients for a class of integrable Schrödinger operators in two dimensions, completing previous partial investigations.

Findings

Explicit Hadamard coefficients derived for 2D integrable Schrödinger operators

Clarifies the connection between these operators and Huygens' principle

Completes prior research on the topic

Abstract

In this note, we compute the Hadamard coefficients of (algebraically) integrable Schrodinger operators in two dimensions. These operators first appeared in [BL] and [B] in connection with Huygens' principle, and our result completes, in a sense, the investigation initiated in those papers.