Title

Conjecture on the Analyticity of PT-Symmetric Potentials and the Reality of their Spectra

Document Type

Article

Publication Date

10-3-2008

Department

Physics and Astronomy

Abstract

The spectrum of the Hermitian Hamiltonian H = p(2) + V (x) is real and discrete if the potential V (x) -> infinity as x -> +/-infinity. However, if V (x) is complex and PT-symmetric, it is conjectured that, except in rare special cases, V (x) must be analytic in order to have a real spectrum. This conjecture is demonstrated by using the potential V (x) = (ix)(a)|x|(b), where a, b are real.

Publication Title

Journal of Physics A-Mathematical and Theoretical

Volume

41

Issue

39