Asymptotic solvability of an imaginary cubic oscillator with spikes

Abstract

For complex potentials V(x) = -(ix)(3) -beta(2)(ix)(-2) - 2betadelta(ix)(1/2) which are PT symmetric, we show that in beta much greater than 1 strong coupling regime the low-lying bound states almost coincide with harmonic oscillators whenever the spectrum remains real (this means, at all delta < delta(critical) (beta) approximate to 1).