Six-Parameter Exponential-Type Potential and the Identity for the Exponential-Type Potentials

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.