The potential (iz)m generates real eigenvalues only, under symmetric rapid decay boundary conditions

DOI10.1063/1.2009667zbMath1110.34009arXivhep-ph/0207251OpenAlexW1665961597MaRDI QIDQ3438550

Kwang C. Shin

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/hep-ph/0207251

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Linear boundary value problems for ordinary differential equations (34B05) Ordinary differential equations in the complex domain (34M99) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (6)

PT-symmetric eigenvalues for homogeneous potentials ⋮ Entire functions with two radially distributed values ⋮ Anharmonic oscillators in the complex plane, \(\mathcal{PT}\)-symmetry, and real eigenvalues ⋮ Entire functions, PT-symmetry and Voros's quantization scheme ⋮ Scattering by infinitely rising one-dimensional potentials ⋮ Topology-controlled spectra of imaginary cubic oscillators in the large-\(\ell \) approach

Cites Work

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• Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
• Generating converging bounds to the (complex) discrete states of theP²+ iX³+ iαXHamiltonian
• Pseudo-Hermiticity versus PT symmetry: The necessary condition for the reality of the spectrum of a non-Hermitian Hamiltonian

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