Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra

Abstract

It is shown that the radial part of the Hydrogen Hamiltonian factorizes as the product of two not mutually adjoint first order differential operators plus a complex constant epsilon. The 1-susy approach is used to construct non-hermitian Hamiltonians with hydrogen spectra. Other non-hermitian Hamiltonians are shown to admit an extra `complex energy' at epsilon. New self-adjoint hydrogen-like Hamiltonians are also derived by using a 2-susy transformation with complex conjugate pairs epsilon, (c.c) epsilon.

LaTeX2e file, 13 pages, 6 EPS figures. New references added. The present is a reorganized and simplified version

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• Generalized coherent states for time-dependent and nonlinear Hamiltonians via complex Riccati equations
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• Gamow-Siegert functions and Darboux-deformed short range potentials
• A Primer on Resonances in Quantum Mechanics
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• On the construction of non-Hermitian Hamiltonians with all-real spectra through supersymmetric algorithms
• Optical potentials using resonance states in Supersymmetric Quantum Mechanics
• Complex SUSY Transformations and the Painlevé IV Equation
• Complex oscillator and Painlevé IV equation
• Quadratic pseudosupersymmetry in two-level systems
• New Exactly Solvable Isospectral Partners for PT Symmetric Potentials
• Rectangular Potentials in a Semi-Harmonic Background: Spectrum, Resonances and Dwell Time
• Extended WKB method, resonances and supersymmetric radial barriers
• Supersymmetry Transformations for Delta Potentials
• Beyond conventional factorization: Non-Hermitian Hamiltonians with radial oscillator spectrum