Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant

G. Andrei Mezincescu

Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant

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arxiv quant-ph/0002056 v1 pith:LQTGUFDK submitted 2000-02-21 quant-ph cond-mathep-thmath-phmath.MP

G. Andrei Mezincescu This is my paper · ORCID

classification quant-phcond-mathep-thmath-phmath.MP

keywords imaginaryeigenfunctionseigenvaluesgammarealbessiscalculationscomparison

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abstract

Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(\pi/5)]\Gamma^2(1/5)/\Gamma(3/5)$, and the results of numeric and WKB calculations supports the conjecture by Bessis that all the eigenvalues of this PT-invariant hamiltonian are real. For one-dimensional Schr\"odinger operators with complex potentials having a monotonic imaginary part, the eigenfunctions (and the imaginary parts of their logarithmic derivatives) have no real zeros.

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Partition Functions of Hermitian and PT-Symmetric Oscillators from Integrable Models
hep-th 2026-08 conditional novelty 5.0 of 10

Partition functions and zeta functions of homogeneous Hermitian and PT-symmetric oscillators are computed from contour integrals of the ODE/IM counting function a(E) obtained from the Destri-de Vega equation.

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