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| related topics |
| {equation, function, exp} |
| {operator, operators, space} |
| {field, particle, equation} |
| {let, theorem, proof} |
|
Darboux transformations and hidden quadratic supersymmetry of the
one-dimensional stationary Dirac equation
N. Debergh, A. A. Pecheritsin, B. F. Samsonov, B. Van den Bossche
abstract: A matricial Darboux operator intertwining two one-dimensional stationary
Dirac Hamiltonians is constructed. This operator is such that the potential of
the second Dirac Hamiltonian as well as the corresponding eigenfunctions are
determined through the knowledge of only two eigenfunctions of the first Dirac
Hamiltonian. Moreover this operator together with its adjoint and the two
Hamiltonians generate a quadratic deformation of the superalgebra subtending
the usual supersymmetric quantum mechanics. Our developments are illustrated on
the free particle case and the generalized Coulomb interaction. In the latter
case, a relativistic counterpart of shape-invariance is observed.
- oai_identifier:
- oai:arXiv.org:quant-ph/0111163
- categories:
- quant-ph
- comments:
- 11 pages, no figure
- arxiv_id:
- quant-ph/0111163
- created:
- 2001-11-30
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