Solvable simulation of a double-well problem in PT symmetric quantum mechanics

Abstract

Within quantum mechanics which works with parity-pseudo-Hermitian Hamiltonians we study the tunneling in a symmetric double well formed by two delta functions with complex conjugate strengths. The model is exactly solvable and exhibits several interesting features. Besides an amazingly robust absence of any PT symmetry breaking, we observe a quasi-degeneracy of the levels which occurs all over the energy range including the high-energy domain. This pattern is interpreted as a manifestation of certain "quantum beats".

12 pages incl. 7 figures

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Cited by in corpus (17)

• Completeness and Orthonormality in PT-symmetric Quantum Systems
• Discrete PT-symmetric models of scattering
• Solvable PT-symmetric model with a tunable interspersion of non-merging levels
• Fragile PT-symmetry in a solvable model
• Solvability and PT-symmetry in a double-well model with point interactions
• Experiments in PT-symmetric quantum mechanics
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• The band spectrum of periodic potentials with PT-symmetry
• Symmetrized quartic polynomial oscillators and their partial exact solvability
• Exactly solvable models with PT-symmetry and with an asymmetric coupling of channels
• The Gram Matrix of a PT-symmetric Quantum System
• The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
• Solvable relativistic quantum dots with vibrational spectra
• Pseudo-invariant approach for a particle in a complex time-dependent linear potential
• Topology-controlled spectra of imaginary cubic oscillators in the large-L approach
• Quasi-Hermitian Hamiltonians associated with exceptional orthogonal polynomials
• The Generalized PT-Symmetric Sinh-Gordon Potential Solvable within Quantum Hamilton-Jacobi Formalism