Calculation of Eigenvalues of a PT Symmetric Complex Cubic Oscillator through Morse-Feshbach Non-Linear Perturbation Series

We study the convergence of the Morse- Feshbach nonlinear perturbation series (MFNPS) series to find out the energy levels of a PT symmetric complex cubic anharmonic oscillator. Perturbation series on energy has been calculated up to 15th order for the ground state and the first excited state. All orders of the MFNPS are found to be real and positive for this non-Hermitian but PT - symmetric Hamiltonian. The convergent energy spectra nicely match with the results of calculation of matrix diagonalization method. Some discussions on wave functions have been made using the nonlinear series.