A Novel Quasi-Exactly Solvable Model with Total Transmission Modes

Details A Novel Quasi-Exactly Solvable Model with Total Transmission Modes A Novel Quasi-Exactly Solvable Model with Total Transmission Modes

2006-06-18

arxiv.org/abs/quant-ph/0606144v4

Physics

Quantum Physics

Revtex, 9 pages, 1 eps figure, claim on continuous bound state spectra removed, more discussions on self-adjoint extensions ad

Scientific paper

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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