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Bulgarian Journal of Physics
Print: 1310-0157 Online: 1314-2666
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RECOGNIZED BY THE EUROPEAN PHYSICAL SOCIETY 
Bulg. J. Phys. vol.53 no.1 (2026), pp. 001-012
Convergent Behaviour of Morse-Feshbach Nonlinear Perturbation Series: Energy Levels of Anharmonic Oscillator
P.K. Samal1, B. Rath2, G. Behera1
1School of Physics, Gangadhar Meher University, Sambalpur 768004, India
2Department of Physics, North Orissa University, Baripada, 757003, India
go back1School of Physics, Gangadhar Meher University, Sambalpur 768004, India
2Department of Physics, North Orissa University, Baripada, 757003, India
Abstract. We make an extensive study on the convergent behaviour of the Morse-Feshbach nonlinear perturbation series (MFNPS) to find out the energy levels of an anharmonic oscillator (AHO) in both weak and strong coupling limits. We developed a new method of multi-step optimal splitting to get convergence in MFNPS for the ground state of AHO and found that two-step optimal splitting is sufficient to provide convergence in MFNPS. Unlike the ground state, the optimal splitting parameters for excited states were modified according to their state dependence to achieve convergence in MFNPS. We apply both single-step and two-step optimal splitting up to the 10th excited states of AHO in both weak and strong coupling limits and achieve a good level of convergence in MFNPS.
doi: https://doi.org/10.55318/bgjp.2026.53.1.001