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Currently, λ is restricted to integers only in the Pöschl-Teller potential. By using a hypergeometric function instead of associated Legendre polynomials for the wave function, it should be possible to generalize λ to non-integer values.
Currently,
λ
is restricted to integers only in the Pöschl-Teller potential. By using a hypergeometric function instead of associated Legendre polynomials for the wave function, it should be possible to generalizeλ
to non-integer values.Please check S. Flügge, Practical Quantum Mechanics (Springer Berlin Heidelberg, 1999) p.94 Problem 39. Potential hole of modified Poschl-Teller type.
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