PT-symmetric quartic anharmonic oscillator and position-dependent mass in a perturbative approach

To lowest order of perturbation theory we show that an equivalence can be established between a $\cal PT$-symmetric generalized quartic anharmonic oscillator model and a Hermitian position-dependent mass Hamiltonian $h$. An important feature of $h$ is that it reveals a domain of couplings where the quartic potential could be attractive, vanishing or repulsive. We also determine the associated physical quantities.