On integrals associated with the Free particle wave packet

Abstract

We discuss some properties of integrals associated with the free particle wave packet, $\psi (x,t),$ which are solutions to the time-dependent Schr$\ddot{o}$dinger equation for a free particle in one dimension. 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.

arXiv commentCorrected Lemma 1.1 and a constant

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