Periodic Quasi - Exactly Solvable Models

Details Periodic Quasi - Exactly Solvable Models Periodic Quasi - Exactly Solvable Models

2004-03-27

arxiv.org/abs/quant-ph/0403196v1

Int. jour. of Theoretical Phys., 44, No. 8, 1167 (2005).

Physics

Quantum Physics

11 pages, 5 tables

Scientific paper

Various quasi-exact solvability conditions, involving the parameters of the periodic associated Lam{\'e} potential, are shown to emerge naturally in the quantum Hamilton-Jacobi approach. It is found that, the intrinsic nonlinearity of the Riccati type quantum Hamilton-Jacobi equation is primarily responsible for the surprisingly large number of allowed solvability conditions in the associated Lam{\'e} case. We also study the singularity structure of the quantum momentum function, which yields the band edge eigenvalues and eigenfunctions.

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