Generation of exactly solvable non-Hermitian potentials with real energies

Abstract

A series of exactly solvable non-trivial complex potentials (possessing real spectra) are generated by applying the Darboux transformation to the excited eigenstates of a non-Hermitian potential V(x). This method yields an infinite number of non-trivial partner potentials, defined over the whole real line, whose spectra are nearly exactly identical to the original potential.

10 pages, 2 figures, Based on the talk presented at the 1st International Workshop "Psedo-Hermitian Hamiltonians in Quantum Physics", held in Prague, June 16, 17, 2003. To be published in Czech. J. Phys. (Jan. 2004)

References in corpus (6)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• PT -symmetric harmonic oscillators
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• Isospectral partners for a complex PT-invariant potential
• Supersymmetric quantum mechanics based on higher excited states

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• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Experiments in PT-symmetric quantum mechanics
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
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• Non-Hermitian Hamiltonian versus E=0 localized states
• Supersymmetric quantum mechanics living on topologically nontrivial Riemann surfaces
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
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• Planarizable Supersymmetric Quantum Toboggans