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New shape invariant potentials in supersymmetric quantum mechanics

Jan 4, 1993
7 pages
Published in:
  • J.Phys.A 26 (1993) L901-L904
e-Print:
DOI:
Report number:
  • PRINT-93-0022 (BHUBANESWAR),
  • IP-BBSR-92-93
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Abstract:
Quantum mechanical potentials satisfying the property of shape invariance are well known to be algebraically solvable. Using a scaling ansatz for the change of parameters, we obtain a large class of new shape invariant potentials which are reflectionless and possess an infinite number of bound states. They can be viewed as q-deformations of the single soliton solution corresponding to the Rosen-Morse potential. Explicit expressions for energy eigenvalues, eigenfunctions and transmission coefficients are given. Included in our potentials as a special case is the self-similar potential recently discussed by Shabat and Spiridonov.
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