2000/02/21 by G. Andrei Mezincescu, G Andrei Mezincescu · 5 citations
Mathematics · Physics and Astronomy · #Mathematical functions and polynomials #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #cond-mat #hep-th #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/33/27/308
published as J.Phys.A33:4911-4916,2000 · 6 pages, submitted to J. Phys. A
arxiv created 2000/02/21 · openalex publication_date 2000/06/27 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
Comparison between the exact value of the spectral zeta function, Z H (1) = 5 -6/5 [3-2cos (π/5)]Γ 2 ((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.