Quasiexactly Solvable Potentails

Details Quasiexactly Solvable Potentails Quasiexactly Solvable Potentails

2003-07-23

arxiv.org/abs/hep-th/0307228v1

Physics

High Energy Physics

High Energy Physics - Theory

M.Sc. Research Thesis. 77 pages, 17 figures

Scientific paper

For quasiexactly solvable (QES) potentials a certain number of wave functions and energy levels can be analytically calculated. The complexity of an explicit calculation of the energy levels grows with the dimension of the QES sector. For a class of such systems the generating function of the secular polynomials is also an initial condition solution of the Schr\"odinger equation. This generating function is used to obtain approximate energy levels in the limit of a large QES sector. This new method combines the WKB approximation with the saddle point approximation.

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