Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
- 27 June 2000
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 33 (27), 4911-4916
- https://doi.org/10.1088/0305-4470/33/27/308
Abstract
Comparison between the exact value of the spectral zeta function, ZH(1) = 5-6/5[3-2cos (π/5)]Γ2((1/5))/Γ((3/5)), and the results of numeric and WKB calculations supports the conjecture by Daniel Bessis (1995 private communication) 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.Keywords
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