On a Class of Non Self-Adjoint Quantum Nonlinear Oscillators with Real Spectrum

AbstractWe prove reality of the spectrum for a class of PT− symmetric, non self-adjoint quantum nonlinear oscillators of the form H=p2+ P(q) + igQ(q). Here P(q) is an even polynomial of degree 2ppositive at infinity, Q(q) an odd polynomial of degree 2r− 1, and the conditions p> 2r, |g| < for some > 0 hold.