2017/01/25 by Cheng Tang, Tang, Cheng, Andrei V. Frolov +1
Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #Neutrino Physics Research #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1701.07180
openalex publication_date 2017/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The real energy spectrum from the PT-symmetric Hamiltonian H = p2 - (ix)N with x∈ℂ was examined within one pair of Stokes wedges in 1998 by Bender and Boettcher. For this Hamiltonian we discuss the following three questions. First, since their paper used a Runge-Kutta method to integrate along a path at the center of the Stokes wedges to calculate eigenvalues E with high accuracy, we wonder if the same eigenvalues can be obtained if integrate along some other paths in different shapes. Second, what the corresponding eigenfunctions look like? Should the eigenfunctions be independent from the shapes of path or not? Third, since for large N the Hamiltonian contains many pairs of Stokes wedges symmetric with respect to the imaginary axis of x, thus multiple families of real energy spectrum can be obtained. What do they look like? Any relation among them?