ON THE REAL TRACE OF SPECTRUM OF AFAMILYOFPT-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.