Isospectral Potentials from Modified Factorization

Details Isospectral Potentials from Modified Factorization Isospectral Potentials from Modified Factorization

2010-08-09

arxiv.org/abs/1008.1528v1

Phys.Rev.A82:022121,2010

Physics

Quantum Physics

8 pages, 4 figures

Scientific paper

10.1103/PhysRevA.82.022121

Factorization of quantum mechanical potentials has a long history extending back to the earliest days of the subject. In the present paper, the non-uniqueness of the factorization is exploited to derive new isospectral non-singular potentials. Many one-parameter families of potentials can be generated from known potentials using a factorization that involves superpotentials defined in terms of excited states of a potential. For these cases an operator representation is available. If ladder operators are known for the original potential, then a straightforward procedure exists for defining such operators for its isospectral partners. The generality of the method is illustrated with a number of examples which may have many possible applications in atomic and molecular physics.

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