Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach

Details Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach Bound States and Band Structure - a Unified Treatment through the Quantum Hamilton - Jacobi Approach

2005-06-24

arxiv.org/abs/quant-ph/0506204v1

Ann of phys, Vol 320, Issue 1, 164 (2005)

Physics

Quantum Physics

12 pages, 2 figures.Accepted for publication in Annals of Physics

Scientific paper

10.1016/j.aop.2005.05.004

We analyze the Scarf potential, which exhibits both discrete energy bound states and energy bands, through the quantum Hamilton-Jacobi approach. The singularity structure and the boundary conditions in the above approach, naturally isolate the bound and periodic states, once the problem is mapped to the zero energy sector of another quasi-exactly solvable quantum problem. The energy eigenvalues are obtained without having to solve for the corresponding eigenfunctions explicitly. We also demonstrate how to find the eigenfunctions through this method.

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