Real spectra in some negative potentials: linear and nonlinear one-dimensional PT-invariant quantum systems

Abstract

We find real spectral behaviour in negative potentials having PT-symmetry in nature. Apart from linear non-polynomial and polynomial operators, we also consider few nonlinear quantum operators. In the case of polynomial operators, we use appropriate supersymmetry Hamiltonians and verify the iso-spectral nature of energy eigenvalues. All the quantum operators are one-dimensional in nature. The present computation on negative quartic operator yields excellent agreement with the previously computed results (Bender and Boettcher in Phys Rev Lett 80:5243, 1998) and equivalent result of Jones and Mateo (Phys Rev D 73:085002, 2006).