THE TEACHING OF MATHEMATICS

THE TEACHING OF MATHEMATICS
Gaussian integrals depending on a quantum parameter in finite dimension
Simone Camosso

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 depend on 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.

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Keywords: Gaussian integral; quantization; special functions; arithmetic-geometric mean.

DOI: 10.57016/TM-ZOVB7625

Pages:  107$-$115     

Volume  XXV ,  Issue  2 ,  2022