Quasiexactly Solvable Potentails
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 Schrödinger 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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