Infinite potential well with a sinusoidal bottom

Details Infinite potential well with a sinusoidal bottom Infinite potential well with a sinusoidal bottom

2008-08-07

arxiv.org/abs/0808.1006v1

J. Math. Phys. 49, 082102 (2008)

Physics

Quantum Physics

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

Scientific paper

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.

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