Schrödinger operators with complex potential but real spectrum

Abstract

Several aspects of complex-valued potentials generating a real and positive spectrum are discussed. In particular, we construct complex-valued potentials whose corresponding Schrödinger eigenvalue problem can be solved analytically.

10, pages, LaTeX 2.09, 6 Postscript figures, uses amsfont, figures available at http://faupt100.physik.uni-erlangen.de/junker/papers95-99.htm

References in corpus (3)

• Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
• Quasi-exactly solvable quartic potential
• SUSY Quantum Mechanics with Complex Superpotentials and Real Energy Spectra

Cited by in corpus (168)

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• Pseudo-Hermiticity versus PT-Symmetry II: A complete characterizatio n of non-Hermitian Hamiltonians with a real spectrum
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• sl(2, C) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
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• Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
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• Conjecture on the Interlacing of Zeros in Complex Sturm-Liouville Problems
• Complex Calogero model with real energies
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• Quasi-Hermiticity in infinite-dimensional Hilbert spaces
• Biorthogonal Quantum Systems
• Nonlinear Supersymmetric Quantum Mechanics: concepts and realizations
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• Conditions for complex spectra in a class of PT symmetric potentials
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
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• Symmetry breaking of solitons in two-dimensional complex potentials
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• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
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• Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
• Non-Hermitian Quantum Mechanics of Non-diagonalizable Hamiltonians: puzzles with self-orthogonal states
• On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction
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• Non-linear Supersymmetry for non-Hermitian, non-diagonalizable Hamiltonians: I. General properties
• New supersymmetry-generated complex potentials with real spectra
• Supersymmetry generated one-way invisible PT-symmetric optical crystals
• Two-dimensional SUSY-pseudo-Hermiticity without separation of variables
• Necessity of PT symmetry for soliton families in one-dimensional complex potentials
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• Invisible defects in complex crystals
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• "Single Ring Theorem" and the Disk-Annulus Phase Transition
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• An analysis of the zero energy states in graphene
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• Phantom universe from CPT symmetric QFT
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• Quasi-Hermitian supersymmetric extensions of a non-Hermitian oscillator Hamiltonian and of its generalizations
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• Hidden Symmetry from Supersymmetry in One-Dimensional Quantum Mechanics
• Exact propagators for complex SUSY partners of real potentials
• Reflectionless PT-symmetric potentials in the one-dimensional Dirac equation
• $\mathcal{P}\mathcal{T}$ Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
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• Effects of non-uniform distributions of gain and loss in photonic crystals
• Complex Supersymmetry in Graphene
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• Balanced Gain-and-Loss Optical Waveguides: Exact Solutions for Guided Modes in Susy-QM
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Double-Scaling Limit of a Broken Symmetry Quantum Field Theory
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models
• Third-order ladder operators, generalized Okamoto and exceptional orthogonal polynomials
• Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
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• Two-level systems: exact solutions and underlying pseudo-supersymmetry
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• New families of non-parity-time-symmetric complex potentials with all-real spectra
• Quantum knots
• Superoscillatory PT-symmetric potentials
• New version of pseudo-hermiticity in the two-sided deformation of Heisenberg algebra
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
• Non-Hermitian CP-Symmetric Dirac Hamiltonians with Real Energy Eigenvalues
• Canonical Expansion of PT-Symmetric Operators and Perturbation Theory
• Dirichlet spectrum of the paradigm model of complex PT-symmetric potential: $V(x)=-(ix{)}^N$
• Pseudo-Hermitian position and momentum operators, Hermitian Hamiltonian, and deformed oscillators
• Planarizable Supersymmetric Quantum Toboggans
• A criterion for the reality of the spectrum of PT symmetric Schroedinger operators with complex-valued periodic potentials
• Balancing gain and loss in symmetrised multi-well potentials
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• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics
• Construction of non-PT-symmetric complex potentials with all-real spectra
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• Charge oscillations in a simple model of interacting magnetic orbits
• PT-symmetry and Integrability
• Path Integral Representations on the Complex Sphere
• Spectral branch points of the Bloch-Torrey operator