Quantum Physics

   

A Quasi-Exactly Solvable Non-Polynomial, Non-Confining Potential Well

Authors: Spiros Konstantogiannis

Using a momentum scale, we construct an n-independent, non-polynomial, symmetrized finite well, which, with the addition of a delta potential with n-dependent coupling, becomes quasi-exactly solvable. Making a polynomial ansatz for the closed-form eigenfunctions, we obtain a three-term recursion relation, from which the known energies are derived and the polynomial coefficients are factorized. The coupling is then written in terms of a continued fraction, which, as n tends to infinity, reveals a triangular symmetry and converges. Finally, the location of the closed-form eigenfunctions is determined and the first ones are examined.

Comments: 49 Pages.

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Submission history

[v1] 2018-01-13 07:54:01

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