A brief description of operators associated to the quantum harmonic oscillator on Schatten-von Neumann classes

TL;DR

This paper investigates Hermite multipliers related to the quantum harmonic oscillator, focusing on their membership in Schatten classes and analyzing their spectral trace properties.

Contribution

It provides new insights into the Schatten class membership and spectral trace of Hermite multipliers associated with the quantum harmonic oscillator.

Findings

Characterization of Schatten class membership for Hermite multipliers

Analysis of spectral trace properties of these operators

Extension of existing theory to broader classes of operators

Abstract

In this note we study pseudo-multipliers associated to the harmonic oscillator (also called Hermite multipliers) belonging to Schatten classes on $L^2(\mathbb{R}^n)$. We also investigate the spectral trace of these operators.