ON THE REAL TRACE OF SPECTRUM OF A FAMILY OFPT-SYMMETRIC HAMILTONIANS

Abstract

In this paper we give an outline on the real part of energy spectrum of non-Hermitian Hamiltonians Hα = p2 +(−q4 +iαq), where α is a real number. It was showed that when α tends to −∞ some pairs of real branches of the spectrum develop into the range of negative energy levels and coalesce before turning into complex conjugate. This phenomenon for cubic oscillators has been described by Delabaere and Trinh (J.Phys. A: Math. Gen. 33 (2000), 8771-8796), and that motivates our present study.