2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/185965Comparison 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. AQuantum PhysicsCondensed MatterHigh Energy Physics - TheoryMathematical Physicstext