Variational Ansatz for PT-Symmetric Quantum Mechanics

Abstract

A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 - (ix)^N with N positive and x complex is presented. Excellent agreement is obtained for the ground state and low lying excited state energy levels and wave functions. We use an energy functional with a three parameter class of PT-symmetric trial wave functions in obtaining our results.

9 pages -- one postscript figure

Cited by in corpus (39)

• Making Sense of Non-Hermitian Hamiltonians
• A new PT symmetric complex Hamiltonian with a real spectra
• Solution of Schwinger-Dyson Equations for $\mathcal{P}\mathcal{T}$-Symmetric Quantum Field Theory
• Space of State Vectors in PT Symmetrical Quantum Mechanics
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the co-ordinate : real spectrum of complex potentials
• Conjecture on the Interlacing of Zeros in Complex Sturm-Liouville Problems
• Complex Calogero model with real energies
• Quantum Complex Henon-Heiles Potentials
• Biorthogonal Quantum Systems
• Numerical Evidence that the Perturbation Expansion for a Non-Hermitian $\mathcal{P}\mathcal{T}$-Symmetric Hamiltonian is Stieltjes
• The Coulomb - harmonic oscillator correspondence in PT-symmetric quantum mechanics
• PT-symetrically regularized Eckart,Poeschl-Teller and Hulthen potentials
• PT symmetry breaking and explicit expressions for the pseudo-norm in the Scarf II potential
• On the eigenproblems of PT-symmetric oscillators
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• PT/Non-PT Symmetric and Non-Hermitian Poschl-Teller-Like Solvable Potentials via Nikiforov-Uvarov Method
• Bound States of Non-Hermitian Quantum Field Theories
• Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models
• Numerical Simulations of PT-Symmetric Quantum Field Theories
• Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformation
• Exactly solvable non-Hermitian Jaynes-Cummings-type Hamiltonian admitting entirely real spectra from supersymmetry
• Two-Point Green's Function in PT-Symmetric Theories
• PT-Symmetric Quantum Theory Defined in a Krein Space
• 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
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Conserved quantities, exceptional points, and antilinear symmetries in non-Hermitian systems
• Anomalous doublets of states in a PT symmetric quantum model
• Supersymmetric Biorthogonal Quantum Systems
• Conserved Correlation in PT -symmetric Systems: Scattering and Bound States
• Conjecture on the analyticity of PT-symmetric potentials and the reality of their spectra
• Non-perturbative calculations for the effective potential of the $PT$ symmetric and non-Hermitian $(-g{\varphi }^4)$ field theoretic model
• A Novel phase in the phase structure of the $(g{\varphi }^4+h{\varphi }^6{)}_{1+1}$ field theoretic model
• Double-Scaling Limit of a Broken Symmetry Quantum Field Theory
• An ansatz for the eigenstates in PT-symmetric quantum mechanics
• New Ansatz for Metric Operator Calculation in Pseudo-Hermitian Field Theory
• Analytic approximation for eigenvalues of a class of $\mathcal{P}\mathcal{T}$ symmetric Hamiltonians
• PT-/non-PT-Symmetric and non-Hermitian Hellmann Potential: Approximate Bound and Scattering States with Any $\ell$-Values
• Computation and Verification of Spectra for Non-Hermitian Systems
• Uncertainty Relation for Pseudo-Hermitian Quantum Systems