Identity for the Exponential-Type Molecule Potentials and the Supersymmetry Shape Invariance

Abstract

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.

Eigenvalues and Eigenfunctions of Woods–saxon Potential in Pt-Symmetric Quantum Mechanics

“…The association of the factorization and the hierarchy of hamiltonian method with SQM formalism has been introduced to obtain the approximate energy spectra of non-exactly solvable potentials, [6,7] as well as the partially solvable, [8,9], the isospectral, [10], the periodic potentials, [11] and the exponential-type potentials [12,13,14,15]. Using the physical arguments, it is possible to make an ansatz for the superpotential which satisfies the Riccati equation by an effective potential.…”