Non-Hermitian matrix description of the PT symmetric anharmonic oscillators

Abstract

Schroedinger equation H ψ=E ψwith PT - symmetric differential operator H=H(x) = p^2 + a x^4 + i βx^3 +c x^2+i δx = H^*(-x) on L_2(-\infty,\infty) is re-arranged as a linear algebraic diagonalization at a>0. The proof of this non-variational construction is given. Our Taylor series form of ψcomplements and completes the recent terminating solutions as obtained for certain couplings δat the less common negative a.

18 pages, latex, no figures, thoroughly revised (incl. title), J. Phys. A: Math. Gen., to appear

Cited by in corpus (19)

• Perturbation theory in a framework of iteration methods
• Shape invariant potentials with PT symmetry
• 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
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformation
• An exactly solvable PT symmetric potential from the Natanzon class
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Should PT symmetric quantum mechanics be interpreted as nonlinear?
• Admissible perturbations and false instabilities in PT-symmetric quantum systems
• PT symmetric models in more dimensions and solvable square-well versions of their angular Schroedinger equations
• Anomalous doublets of states in a PT symmetric quantum model
• Solvable PT symmetric Hamiltonians
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism
• Discrete spectrum of thin PT-symmetric waveguide
• Point Interactions: PT-Hermiticity and Reality of the Spectrum
• Eigenvalues collision for PT-symmetric waveguide
• Quasi-Hermitian quantum mechanics and a new class of user-friendly matrix Hamiltonians