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A Novel Quasi-Exactly Solvable Model with Total Transmission Modes

Hing-Tong Cho·Choon-Lin Ho
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Abstract

In this paper we present a novel quasi-exactly solvable model with symmetric inverted potentials which are unbounded from below. The quasi-exactly solvable states are shown to be total transmission (or reflectionless) modes. From these modes even and odd wavefunctions can be constructed which are normalizable and flux-zero. Under the procedure of self-adjoint extension, a discrete spectrum of bound states can be obtained for these inverted potentials and the solvable part of the spectrum is the quasi-exactly solvable states we have discovered.

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Hing-Tong Cho, Choon-Lin Ho. 2008-06-10. A Novel Quasi-Exactly Solvable Model with Total Transmission Modes. https://arxiv.org/abs/quant-ph/0606144

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