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On integrals associated with the free particle wave packet

Patkowski Alexander E.

Journal of Applied Analysis

2020

Vol. 26, nr 2

257--262

We discuss some properties of integrals associated with the free particle wave packet, ψ(x, t), which are solutions to the time-dependent Schrödinger equation for a free particle. Some noteworthy discussion is made in relation to integrals which have appeared in the literature. We also obtain formulas for half-integer arguments of the Riemann zeta function.

On some non-Gaussian wave packets

Patkowski A. E.

Journal of Applied Analysis

2018

Vol. 24, nr 1

109--114

We expand on a previous study by offering a generalized wave function associated with the parabolic cylinder function and a connection with a two-particle position-space wave function. We also provide an explicit formula for a wave function associated with a recent work by the present author and M. Wolf.