PT-symmetric cubic anharmonic oscillator as a physical model

  title={PT-symmetric cubic anharmonic oscillator as a physical model},
  author={Ali Mostafazadeh},
  journal={Journal of Physics A},
There is a factor of 2 error in equation (61) of this paper. Correcting this error leads to minor changes in equations (62) and (63). Please see PDF for details. 

Figures from this paper

a Perturbative Treatment of a Generalized {PT}-SYMMETRIC Quartic Anharmonic Oscillator
We examine a generalized -symmetric quartic anharmonic oscillator model to determine the various physical variables perturbatively in powers of a small quantity e. We make use of the Bender–Dunne
symmetric effective mass Schrödinger equations
We outline a general method of obtaining exact solutions of -symmetric Schrodinger equations with a position-dependent effective mass. Using this method, exact solutions of some -symmetric potentials
- symmetry and Integrability ∗
We briefly explain some simple arguments based on pseudo Hermiticity, supersymmetry and PT -symmetry which explain the reality of the spectrum of some non-Hermitian Hamiltonians. Subsequently we
Closed formula for the metric in the Hilbert space of a -symmetric model
We introduce a very simple, exactly solvable -symmetric non-Hermitian model with a real spectrum, and derive a closed formula for the metric operator which relates the problem to a Hermitian one.
Path-integral formulation of pseudo-Hermitian quantum mechanics and the role of the metric operator
We provide a careful analysis of the generating functional in the path-integral formulation of pseudo-Hermitian and in particular PT-symmetric quantum mechanics and show how the metric operator
LETTER TO THE EDITOR: Pseudo-Hermiticity and some consequences of a generalized quantum condition
We exploit the hidden symmetry structure of a recently proposed non-Hermitian Hamiltonian and of its Hermitian equivalent one. This sheds new light on the pseudo-Hermitian character of the former and
A squeeze-like operator approach to position-dependent mass in quantum mechanics
We provide a squeeze-like transformation that allows one to remove a position dependent mass from the Hamiltonian. Methods to solve the Schrodinger equation may then be applied to find the respective


Pseudo-Hermiticity versus PT-symmetry. II. A complete characterization of non-Hermitian Hamiltonians with a real spectrum
We give a necessary and sufficient condition for the reality of the spectrum of a non-Hermitian Hamiltonian admitting a complete set of biorthonormal eigenvectors.
Perturbation theory of odd anharmonic oscillators
We study the perturbation theory forH=p2+x2+βx2n+1,n=1, 2, .... It is proved that when Imβ≠0,H has discrete spectrum. Any eigenvalue is uniquely determined by the (divergent) Rayleigh-Schrödinger
Real Spectra in Non-Hermitian Hamiltonians Having PT Symmetry
The condition of self-adjointness ensures that the eigenvalues of a Hamiltonian are real and bounded below. Replacing this condition by the weaker condition of $\mathrm{PT}$ symmetry, one obtains new
PT-symmetric Quantum Mechanics: A Precise and Consistent Formulation
The physical condition that the expectation values of physical observables are real quantities is used to give a precise formulation of PT-symmetric quantum mechanics. A mathematically rigorous proof
Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian
A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian H=p2+14x2+iλx3, is performed using high-order Rayleigh–Schrodinger perturbation theory. The energy spectrum of
Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
Comparison between the exact value of the spectral zeta function, ZH(1) = 5-6/5[3-2cos (π/5)]Γ2((1/5))/Γ((3/5)), and the results of numeric and WKB calculations supports the conjecture by Daniel
Pseudo-Hermitian description of PT-symmetric systems defined on a complex contour
We describe a method that allows for a practical application of the theory of pseudo-Hermitian operators to PT-symmetric systems defined on a complex contour. We apply this method to study the
Calculation of the hidden symmetry operator in -symmetric quantum mechanics
In a recent paper it was shown that if a Hamiltonian H has an unbroken symmetry, then it also possesses a hidden symmetry represented by the linear operator . The operator commutes with both H and .
On the Reality of the Eigenvalues for a Class of -Symmetric Oscillators
Abstract We study the eigenvalue problem with the boundary conditions that decays to zero as z tends to infinity along the rays , where is a real polynomial and . We prove that if for some we have
Exact PT-symmetry is equivalent to Hermiticity
We show that a quantum system possessing an exact antilinear symmetry, in particular PT-symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator