Second-order supersymmetric operators and excited states

Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well developed. We demonstrate that the existence of raising and lowering operators for the...

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Bibliographic Details
Published inJournal of physics. A, Mathematical and theoretical Vol. 43; no. 38; p. 385309
Main Authors Berger, Micheal S, Ussembayev, Nail S
Format Journal Article
LanguageEnglish
Published Bristol IOP Publishing 24.09.2010
IOP
Subjects
Chains
Density
Exact sciences and technology
Factorization
Ladders
Mathematical analysis
Operators
Physics
Quantum mechanics
Wavefunctions
Operator
Probability density
Second order
Supersymmetry
Hamiltonians
Wave functions
Excited states
Factorization
Supersymmetric quantum mechanics
Complexity
Harmonic oscillators
Singular potential
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Summary:Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well developed. We demonstrate that the existence of raising and lowering operators for the harmonic oscillator (and many other potentials) can be extended to their supersymmetric partners. The double supersymmetry (or a factorization chain) is used to obtain non-singular isospectral potentials, and the explicit expressions for the ladder operators, wavefunctions and probability densities are provided. This application avoids the technical complexities of the most general approaches, and requires relatively modest methods from supersymmetric quantum mechanics.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:1751-8121
1751-8113
1751-8121
DOI:10.1088/1751-8113/43/38/385309