New Fourier transform containing a pair of complex Euler Gamma-functions with a monomial: Mathematical and physical applications

摘要

One of the goals of this paper is to propose an elementary method to find a general formula for a new Fourier transform containing a pair of complex Euler Gamma-functions with a monomial s(m) in terms of Gauss's hypergeometric functions F-2(1). Some mathematical results have been obtained and discussed using this transform. Furthermore, physical applications in the phase space quantum mechanics requiring the expectation values of position and momentum operators for a quantum system endowed with position-dependent effective mass are presented. Published by AIP Publishing.