Some properties of eigenvalues and eigenfunctions of the cubic oscillator with imaginary coupling constant
Abstract
Description
Comparison between the exact value of the spectral zeta function, $Z_{H}(1)=5^{-6/5}[3-2\cos(π/5)]Γ^2(1/5)/Γ(3/5)$, 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
6 pages, submitted to J. Phys. A