Gaussian integrals depending by a quantum parameter in finite dimension

TL;DR

This paper explores a specific class of Gaussian integrals that depend on the quantum parameter 5, providing an overview of methods and examples for solving quantum Gaussian integrals in finite dimensions.

Contribution

It introduces and analyzes quantum-dependent Gaussian integrals, offering new insights and methods for their evaluation in finite-dimensional spaces.

Findings

Overview of classical and quantum Gaussian integral methods

Examples illustrating quantum Gaussian integral evaluations

Analogies connecting classical and quantum cases

Abstract

A common theme in mathematics is the evaluation of Gauss integrals. This, coupled with the fact that they are used in different branches of science, makes the topic always actual and interesting. In these notes we shall analyze a particular class of Gaussian integrals that depends by the quantum parameter $\hbar$. Starting from classical results, we will present an overview on methods, examples and analogies regarding the practice of solving quantum Gaussian integrals.