ISSN:
1432-2234
Keywords:
Key words: Isospectral Hamiltonians
;
Darboux's transformation
;
Molecular potentials
;
Schroedinger equation
Source:
Springer Online Journal Archives 1860-2000
Topics:
Chemistry and Pharmacology
Notes:
Abstract. A generalization of the Hulthén potential is presented on the basis of an approach that uses the factorization of a general Hamiltonian by means of a specific model of operational equations with the structure ∼β(r)∓(d/dr). To achieve this goal, the treatment of the V Hs(r) standard Hulthén potential for bound s states is carried out by proposing a particular βp(r) ansatz to identify V Hs(r) by means of a particular Riccati-type relationship. Once the identification has been achieved, the generalized Hulthén potential is obtained straightforwardly with the aid of a general Riccati formula. As expected, the Hamiltonian of the generalized Hulthén potential is isospectral when compared with the corresponding standard Hamiltonian. Moreover, according to the Darboux transform there exists a modified Hulthén potential which is also isospectral. We show that the latter is just a particular case of the generalized Hulthén interaction model.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002140000130
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