A unified recurrence operator method for obtaining normalized explicit wavefunctions for shape-invariant potentials. (English) Zbl 0931.34070
Summary: The authors construct a unified recurrence operator method for obtaining explicit expressions for the wavefunctions of shape-invariant potentials. It is found that the normalized coefficients for the energy eigenfunctions satisfy a universal recurrence relation.
The procedure is illustrated in detail for four potentials. The authors worked out the normalized explicit wavefunctions of Hulthen potential, for which the normalized explicit wavefunctions have not been previously calculated.
The procedure is illustrated in detail for four potentials. The authors worked out the normalized explicit wavefunctions of Hulthen potential, for which the normalized explicit wavefunctions have not been previously calculated.
MSC:
| 34L40 | Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
