Bound state solutions of the Schrödinger equation for a \(\mathcal{PT}\)-symmetric potential with Dirac delta functions

DOI10.1016/J.PHYSLETA.2006.06.034zbMath1236.81089OpenAlexW2056440057MaRDI QIDQ942556

Ersan Demiralp, Haydar Uncu

Publication date: 5 September 2008

Published in: Physics Letters. A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physleta.2006.06.034

Mathematics Subject Classification ID

Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05)

Related Items (4)

\(\mathcal{PT}\)-symmetric peakon solutions in self-focusing/defocusing power-law nonlinear media: stability, interactions and adiabatic excitations ⋮ Localised Nonlinear Modes in the PT-Symmetric Double-Delta Well Gross-Pitaevskii Equation ⋮ Stable solitons and peakons, quantum information entropies, interactions, and excitations for generalized \(\mathcal{PT}\)-symmetric NLS equations ⋮ PSEUDO-HERMITIAN REPRESENTATION OF QUANTUM MECHANICS

Cites Work

• Symmetries of Schrödinger operators with point interactions
• PT-symmetry in one-dimensional quantum periodic potentials
• Point interactions: \(\mathcal{PT}\)-Hermiticity and reality of the spectrum.
• Trigonometric identities, angular Schrödinger equations and a new family of solvable models
• Fragile PT-symmetry in a solvable model
• Must a Hamiltonian be Hermitian?
• Properties of bound states of the Schr dinger equation with attractive Dirac delta potentials
• ExactPT-symmetry is equivalent to Hermiticity
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• The band spectrum of periodic potentials with Script PScript T-symmetry
• Statistical origin of pseudo-Hermitian supersymmetry and pseudo-Hermitian fermions
• Physical aspects of pseudo-Hermitian andPT-symmetric quantum mechanics
• Properties of a pseudo-Hermitian Hamiltonian for harmonic oscillator decorated with Dirac delta interactions
• An explicitly solvable model of the spontaneous PT-symmetry breaking
• -invariant point interactions in one dimension
• One-dimensional Schrödinger operators with -symmetric zero-range potentials
• Solvability and -symmetry in a double-well model with point interactions
• Energy band structure due to a complex, periodic, PT-invariant potential

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