Periodic Quasi - Exactly Solvable Models

S. Sree Ranjani, A. K. Kapoor, P. K. Panigrahi

Published 2004-03-27Version 1

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.