Infinite potential well with a sinusoidal bottom

Abstract

We construct a tridiagonal matrix representation of the wave operator that maps the wave equation into a three-term recursion relation for the expansion coefficients of the wavefunction. Finding a solution of the recursion relation is equivalent to solving the original problem. Consequently, a larger class of solvable potentials is obtained. The usual diagonal representation constraint results in a reduction to the conventional class of solvable potentials. To exhibit the power of this approach, we give an exact solution for the infinite potential well with sinusoidal bottom.

8 pages, 2 figures, 1 table Details will be published in Journal of Mathematical Physics, Vol. 49, Issue 8 (August 2008)

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• Bound states of a short-range potential with inverse cube singularity
• Exact solvability of two new 3D and 1D nonrelativistic potentials within the TRA framework
• Electric dipole and quadrupole contributions to valence electron binding in a charge-screening environment
• Five-parameter potential box with inverse square singular boundaries
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