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

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 Schrödinger operators with complex potentials having a monotonic imaginary part, the eigenfunctions (and the imaginary parts of their logarithmic derivatives) have no real zeros.

6 pages, submitted to J. Phys. A

References in corpus (1)

• Distributional Borel Summability of Odd Anharmonic Oscillators

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