On the eigenproblems of PT-symmetric oscillators

DOI10.1063/1.1366328zbMath1016.81023arXivmath-ph/0007006OpenAlexW3101723301MaRDI QIDQ2774913

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Publication date: 26 February 2002

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0007006

zbMATH Keywords

non-Hermitian Hamiltonian

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

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Cites Work

• PT-symmetric sextic potentials
• Approximate analytical states of a polynomial potential: an example of symmetry restoration
• Perturbation theory of odd anharmonic oscillators
• Variational ansatz for PT-symmetric quantum mechanics
• Conjecture on the interlacing of zeros in complex Sturm–Liouville problems
• 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
• Large-order perturbation theory for a non-Hermitian 𝓟𝓣-symmetric Hamiltonian
• Distributional Borel summability of odd anharmonic oscillators
• Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
• 𝓟𝓣-symmetric quantum mechanics