A New Class of PT-symmetric Hamiltonians with Real Spectra

Abstract

We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY Quantum Mechanics providing a partnership between a real and a complex PT-symmetric potential of the kind mentioned above. We investigate conditions sufficient to ensure the reality of the full spectrum or, for the quasi-exactly solvable systems, the reality of the energy of the finite number of levels.

9 pages, Latex

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Cited by in corpus (30)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
• Pseudo-Hermiticity versus PT-Symmetry III: Equivalence of pseudo-Her miticity and the presence of antilinear symmetries
• The ODE/IM Correspondence
• Pseudo-Supersymmetric Quantum Mechanics and Isospectral Pseudo-Hermi tian Hamiltonians
• Supersymmetry-generated complex optical potentials with real spectra
• Fermionic coherent states for pseudo-Hermitian two-level systems
• PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential
• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• Complex Optical Potentials and Pseudo-Hermitian Hamiltonians
• Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
• Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
• A new class of non-Hermitian Hamiltonians with real spectra
• An exactly solvable PT symmetric potential from the Natanzon class
• Isospectral partners for a complex PT-invariant potential
• Factorization and superpotential of the PT symmetric Hamiltonian
• Supersymmetrical Separation of Variables in Two-Dimensional Quantum Mechanics
• Linear representation of energy-dependent Hamiltonians
• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
• Quadratic pseudosupersymmetry in two-level systems
• PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework
• Equivalent Hermitian operator from supersymmetric quantum mechanics
• Lower bound of minimal time evolution in quantum mechanics
• Two-level systems: exact solutions and underlying pseudo-supersymmetry
• Supersymmetric approach to exact solutions of $(1+1)$-dimensional time-independent Klein-Gordon equation : Application to a position-dependent mass and a $\mathcal{P}\mathcal{T}$-symmetric vector potential
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• The ODE/IM correspondence and PT-symmetric quantum mechanics