A class of exactly solvable potentials related to the Jacobi polynomials
| Autor: | G Levai |
|---|---|
| Rok vydání: | 1991 |
| Předmět: |
Pure mathematics
Class (set theory) General Physics and Astronomy Statistical and Nonlinear Physics Connection (mathematics) Algebra symbols.namesake Domain (ring theory) Energy spectrum Bound state symbols Jacobi polynomials Supersymmetric quantum mechanics Wave function Mathematical Physics Mathematics |
| Zdroj: | Journal of Physics A: Mathematical and General. 24:131-146 |
| ISSN: | 1361-6447 0305-4470 |
| DOI: | 10.1088/0305-4470/24/1/022 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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