The author investigates a family of solvable potentials related to the Jacobi polynomials. This one-dimensional potential family depends on three parameters and is restricted to the domain XO, so it can be interpreted as the radial part of a central potential in three dimensions (with l=0). Closed expressions are obtained for the bound state energy spectrum and the wavefunctions. The supersymmetric partner of this potential is also determined and it is found not to belong to the same potential family. It is shown that this potential family is a special subclass of the general six-parameter Natanzon potential class and similarities with another subclass, the Ginocchio potentials, are pointed out. Some aspects of supersymmetric quantum mechanics and shape invariance are also discussed in connection with the potential family under study.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)