Non-Hermitian Hamiltonians with real and complex eigenvalues in a Lie-algebraic framework
arXiv:math-ph/0205002 · doi:10.1016/S0375-9601(02)00689-8
Abstract
We show that complex Lie algebras (in particular sl(2,C)) provide us with an elegant method for studying the transition from real to complex eigenvalues of a class of non-Hermitian Hamiltonians: complexified Scarf II, generalized Pöschl-Teller, and Morse. The characterizations of these Hamiltonians under the so-called pseudo-Hermiticity are also discussed.
LaTeX, 14 pages, no figure, 1 reference added
References in corpus (9)
- 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
- Generalized Continuity Equation and Modified Normalization in PT-Symmetric Quantum Mechanics
- Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
- Conditions for complex spectra in a class of PT symmetric potentials
- Spontaneous breakdown of PT symmetry in the solvable square-well model
- Complexified PSUSY and SSUSY interpretations of some PT-symmetric Hamiltonians possessing two series of real energy eigenvalues
- A PT Symmetric QES Partner to the Khare Mandal Potential With Real Eigen Values
- PT-symmetric non-polynomial oscillators and hyperbolic potential with two known real eigenvalues in a SUSY framework
Cited by in corpus (48)
- Complex Extension of Quantum Mechanics
- Nonlinear waves in -symmetric systems
- Introduction to PT-Symmetric Quantum Theory
- A General Approach for the Exact Solution of the Schrodinger Equation
- Must a Hamiltonian be Hermitian?
- Extension of PT-Symmetric Quantum Mechanics to Quantum Field Theory with Cubic Interaction
- Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry
- The C Operator in PT-Symmetric Quantum Theories
- Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method
- Bound states of the Dirac equation for the PT-symmetric generalized Hulthen potential by the Nikiforov-Uvarov method
- Bound states, scattering states and resonant states in PT-symmetric open quantum systems
- Exponential Type Complex and non-Hermitian Potentials in PT-Symmetric Quantum Mechanics
- Semiclassical Calculation of the C Operator in PT-Symmetric Quantum Mechanics
- An update on PT-symmetric complexified Scarf II potential, spectral singularities and some remarks on the rationally-extended supersymmetric partners
- Beyond the WKB approximation in PT-symmetric quantum mechanics
- PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
- Jamming anomaly in -symmetric systems
- Solvable PT-symmetric model with a tunable interspersion of non-merging levels
- Non-Hermitian SUSY Hydrogen-like Hamiltonians with real spectra
- New Quasi-Exactly Solvable Sextic Polynomial Potentials
- Relativistic supersymmetric quantum mechanics based on Klein-Gordon equation
- Parametric symmetries in exactly solvable real and P T symmetric complex potentials
- Generalized Swanson models and their solutions
- Analytically Solvable PT-Invariant Periodic Potentials
- Solvable simulation of a double-well problem in PT symmetric quantum mechanics
- Supersymmetric solution of PT-/non-PT-symmetric and non-Hermitian Morse potential is studied to get real and Supersymmetric Solution of PT-/Non-PT-Symmetric and Non-Hermitian Morse Potential via Hamiltonian Hierarchy Method
- Group theoretic approach to rationally extended shape invariant potentials
- PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
- Real spectra for non-Hermitian Dirac equation in 1+1 dimensions with a most general coupling
- Pseudo supersymmetric partners for the generalized Swanson model
- Scattering amplitudes for the rationally extended P T symmetric complex potentials
- PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
- PT-symmetric supersymmetry in a solvable short-range model
- A short note on "Group theoretic approach to rationally extended shape invariant potentials" [Annals of Physics 359, 46 (2015)]
- Exact Solutions of the Schrödinger Equation with position-dependent effective mass via general point canonical transformation
- Symmetric Hamiltonian Model and Dirac Equation in 1+1 dimensions
- Thermodynamic properties of a charged particle in non-uniform magnetic field
- symmetric models with nonlinear pseudo supersymmetry
- A Novel SUSY Energy Bound States Treatment of the Klein-Gordon Equation with PT-Supersymmetric and q-Deformed Hulthen Potential
- Supersymmetric Analysis of the Dirac-Weyl Operator within PT Symmetry
- Comment on `Supersymmetry, PT-symmetry and spectral bifurcation'
- So (2, 1) algebra, local Fermi velocity, and position-dependent mass Dirac equation
- Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
- Supersymmetric Extension of Non-Hermitian su(2) Hamiltonian and Supercoherent States
- New families of non-parity-time-symmetric complex potentials with all-real spectra
- Relativistic Potentials with Rational Extensions
- Supersymmetry of - symmetric tridiagonal Hamiltonians
- Supersymmetric solutions of PT-/non-PT-symmetric and non-Hermitian Screened Coulomb potential via Hamiltonian hierarchy inspired variational method