Asymptotic solvability of an imaginary cubic oscillator with spikes

Abstract

For the PT symmetric potential of Dorey, Dunning and Tateo we show that in the large angular momentum (i.e., strongly spiked) limit the low-lying eigenstates of this popular non-Hermitian problem coincide with the shifted Hermitian harmonic oscillators calculated at the zero angular momentum. This type of an approximate Hermitization is valid in all the domain where the spectrum of energies remains real. It proves very efficient numerically. The construction is asymmetric with respect to the sign of the subdominant square-root spike, and exhibits a discontinuity at the point where the PT symmetric regularization vanishes.

20 pages and 2 figures

References in corpus (4)

• Pseudo-Hermiticity versus PT Symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian
• Spectral equivalences, Bethe Ansatz equations, and reality properties in PT-symmetric quantum mechanics
• Non-Hermitian supersymmetry and singular PT symmetrized oscillators
• Spiked harmonic oscillators

Cited by in corpus (26)

• A new deformed Schioberg-type potential and ro-vibrational energies for some diatomic molecules
• PT symmetric pseudo-perturbation recipe; an imaginary cubic oscillator with spikes
• (1+1)-Dirac particle with position-dependent mass in complexified Lorentz scalar interactions: effectively PT-symmetric
• $\eta$-weak-Pseudo-Hermiticity generators and exact solvability
• Non-Hermitian d-dimensional Hamiltonians with position dependent mass and their $\eta$-pseudo-Hermiticity generators
• Dirac and Klein-Gordon particles in complex Coulombic fields; a similarity transformation
• Solvable simulation of a double-well problem in PT symmetric quantum mechanics
• Non-Hermitian von Roos Hamiltonian's $\eta$-weak-pseudo-Hermiticity, isospectrality and exact solvability
• First-order intertwining operators with position dependent mass and $\eta$- weak-psuedo-Hermiticity generators
• Energy bounds for a class of singular potentials and some related series
• Energy-levels crossing and radial Dirac equation: Supersymmetry and quasi-parity spectral signatures
• PT-symmetric supersymmetry in a solvable short-range model
• Position-dependent mass charged particles in magnetic and Aharonov-Bohm flux fields: separability, exact and conditionally exact solvability
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Perturbation method for non-square Hamiltonians and its application to polynomial oscillators
• Non-Hermitian Hamiltonian versus E=0 localized states
• Reply to the Comment 'On large-N expansion'
• Dynamics of charged fluids and 1/L perturbation expansions
• Klein-Gordon particles in Gödel-type Som-Raychaudhuri cosmic string spacetime and the phenomenon of spacetime associated degeneracies
• $\eta$-weak-pseudo-Hermiticity generators and radially symmetric Hamiltonians
• Quasi-exact minus-quartic oscillators in strong-core regime
• Spherical-separablility of non-Hermitian Dirac Hamiltonians and pseudo-PT-symmetry
• Spherical-separablility of non-Hermitian Hamiltonians and pseudo-PT-symmetry
• Ad hoc physical Hilbert spaces in Quantum Mechanics
• The large-g observability of the low-lying energies in the strongly singular potentials $V(x)=x^2+g^2/x^6$ after their PT-symmetric regularization
• Planarizable Supersymmetric Quantum Toboggans