The exact eigenfunctions and eigenvalues of a particle in a box obtained using Gaussian wavepacket dynamics

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Abstract
Exact eigenfunctions for a particle in a box are obtained using Gaussian wavepacket dynamics. The eigenfunctions are obtained by propagating, without approximation, an infinite set of Gaussian wavepackets that collectively satisfy the boundary conditions of the problem, being coherent states appropriate to this problem. The method of images is applied to enforce these boundary conditions. This technique may be applied to the quantum billiard problem whenever the particle is confined to any open or closed region that tessellates space, regardless of the dimension of the region. Also, it is shown that the use of frozen Gaussians along with the De Leon-Heller spectral quantisation method gives the exact solution for the one-dimensional problem as well as for the above multi-dimensional problems, provided the components of the momentum of the wavepackets are chosen at random.