PT-symmetric pseudo-perturbation recipe: an imaginary cubic oscillator with spikes

2002/06/30 by Omar Mustafa, Miloslav Znojil · 2 citations
Mathematics · Physics and Astronomy · #Interval (graph theory) #Noise (video) #Nonlinear Waves and Solitons #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #State (computer science) #Upper and lower bounds #Work (physics) #math-ph #math.MP #math.SP

paper · pdf · doi:10.1088/0305-4470/35/42/304

published as J.Phys.A35:8929,2002 · Revtex file, 22 pages, 2 ps figures, submitted for publication (JPA)

arxiv created 2002/08/24 · openalex publication_date 2002/10/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The pseudo-perturbative shifted-ℓ expansion technique (PSLET) is shown to be applicable in the non-Hermitian 𝒫𝒯-symmetric context. The construction of bound states for several 𝒫𝒯-symmetric potentials is presented, with special attention paid to V ( r ) = i r 3 − α√i r oscillators.

Citations

• sl(2, ) as a complex Lie algebra and the associated non-Hermitian Hamiltonians with real eigenvalues
• Conditions for complex spectra in a class of PT symmetric potentials
• Quasi-relativistic harmonic oscillator bound states
• Vortex pinning and non-Hermitian quantum mechanics
• Non-Hermitian localization and delocalization
• Bound states for spiked harmonic oscillators and truncated Coulomb potentials
• Non-Hermitian matrix description of the calPcalT-symmetric anharmonic oscillators
• Real Spectra in Non-Hermitian Hamiltonians HavingPTSymmetry
• Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
• A PT-invariant potential with complex QES eigenvalues
• Solution of Schwinger-Dyson Equations for \cal PT-Symmetric Quantum Field Theory

Cited by

• η-weak-pseudo-Hermiticity generators and exact solvability
• Pseudo-reality and pseudo-adjointness of Hamiltonians