Generation of a Novel Exactly Solvable Potential

Abstract

We report a new shape invariant (SI) isospectral extension of the Morse potential. Previous investigations have shown that the list of "conventional" SI superpotentials that do not depend explicitly on Planck's constant $\hslash$ is complete. Additionally, a set of "extended" superpotentials has been identified, each containing a conventional superpotential as a kernel and additional $\hslash$-dependent terms. We use the partial differential equations satisfied by all SI superpotentials to find a SI extension of Morse with novel properties. It has the same eigenenergies as Morse but different asymptotic limits, and does not conform to the standard generating structure for isospectral deformations.

9 pages, 3 figures

References in corpus (4)

• Exceptional orthogonal polynomials, exactly solvable potentials and supersymmetry
• Solvable Rational Potentials and Exceptional Orthogonal Polynomials in Supersymmetric Quantum Mechanics
• Novel Enlarged Shape Invariance Property and Exactly Solvable Rational Extensions of the Rosen-Morse II and Eckart Potentials
• Shape Invariant Rational Extensions And Potentials Related to Exceptional Polynomials

Cited by in corpus (8)

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• Numerical study of the SWKB condition of novel classes of exactly solvable systems
• Deformed Shape Invariant Superpotentials in Quantum Mechanics and Expansions in Powers of $\hslash$
• Solvable Schrodinger Equations of Shape Invariant Potentials Having Superpotential W(x,A,B)=Atanh(px)+Btanh(6px)