We present the energy eigenvalues of modified Pschl-Teller potential,the N-dimensionalhydrogen atom,and the N-dimensional harmonic oscillator.The calculations are carried out in the framework of supersymmetry and shape invariance.The present energy spectrum formulas are consistent with the exact solutions obtained with the usual factorization method.
The identity and the supersymmetry shape invariance for a class of exponential-type molecule potentials are studied by introducing a deformed five-parameter exponential-type potential (DFPEP) and via the multi-parameter deformations. It has been shown that the DFPEP is a shape-invariant potential with a translation of parameters. By making use of the shape invariance approach, the exact energy levels are determined for the bound states with zero angular momentum. A class of molecule potentials and their exact energy spectra for the zero angular momentum states are reduced from the DFPEP and a general energy spectrum formula, respectively. The interrelations for some molecule potentials are also discussed.
We propose a six-parameter exponential-type potential (SPEP), which has been shown to be a shape-invariant potential with a translation of parameters. For this reducible potential, the exact energy levels are obtained by using the supersymmetric shape invariance technique. Choosing appropriate parameters, four classes of exponential-type potentials and their exact energy spectra are reduced from the SPEP and a general energy level formula, respectively. Each class shows the identity except for the different definitions of parameters.
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