Physics – Quantum Physics
Scientific paper
2001-02-19
Int.J.Mod.Phys. A16 (2001) 2859-2872
Physics
Quantum Physics
20 pages, Latex 2e + amssym + graphics, 2 figures, accepted in Int. J. Mod. Phys. A
Scientific paper
10.1142/S0217751X01004153
In the framework of SUSYQM extended to deal with non-Hermitian Hamiltonians, we analyze three sets of complex potentials with real spectra, recently derived by a potential algebraic approach based upon the complex Lie algebra sl(2, C). This extends to the complex domain the well-known relationship between SUSYQM and potential algebras for Hermitian Hamiltonians, resulting from their common link with the factorization method and Darboux transformations. In the same framework, we also generate for the first time a pair of elliptic partner potentials of Weierstrass $\wp$ type, one of them being real and the other imaginary and PT symmetric. The latter turns out to be quasiexactly solvable with one known eigenvalue corresponding to a bound state. When the Weierstrass function degenerates to a hyperbolic one, the imaginary potential becomes PT non-symmetric and its known eigenvalue corresponds to an unbound state.
Bagchi Bhaskar
Mallik Sudipta
Quesne Christiane
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