ISSN:
1434-6079
Keywords:
PACS. 03.65.Ge Solutions of wave equations: bound states
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract: A transformation method has been applied to the exactly solvable Hulthen problem to generate a hierarchy of exactly solved quantum systems in any chosen dimension. The generated quantum systems are, in general, energy-dependent with a single normalized eigenfunction, as the Hulthen potential is a non-powerlaw potential. A method has been devised to convert a subset of the generated quantum systems with energy-dependent potentials to a single normal system with an energy-independent potential that behaves like a potential qualitatively similar to the Poschl-Teller potential. A second-order application of the transformation method on the Hulthen system produces another Sturmian quantum system and a different method is given to regroup them into a normal quantum system which resembles the Morse potential. Existence of normalizable eigenfunctions for these systems are found to be dependent on the local and asymptotic behaviour of the transformation function.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s100530170032
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