Eur. Phys. J. Plus (2022) 137: 327
https://doi.org/10.1140/epjp/s13360-022-02528-7

Regular Article

Energy spectra of the spiked harmonic oscillator using the shifted 1/N expansion

Department of Physics, Faculty of Science, Al-Balqa Applied University, Al Salt, Jordan

^b sandouqa@bau.edu.jo

Received: 30 October 2021
Accepted: 26 February 2022
Published online: 10 March 2022

Abstract

In this work, the three-dimensional quantum spiked harmonic oscillator Hamiltonian family is investigated using the shifted 1/N expansion method, where N is the number of spatial dimensions. Using this method, the energy eigenvalues and the equilibrium interparticle distances of the ground state and the first five excited states of the system are obtained for different values of the coupling constant $\lambda$ and the singularity order $\alpha$. The validity of this method was tested by comparing our results for the ground state with results obtained using other techniques. For small and intermediate magnitudes of $\lambda$, the energy eigenvalues slightly deviate from the quantum harmonic oscillators. For large $\lambda$, the changes are significant. We found that the energy eigenvalues become negative in the Coulomb region $\lambda \ll -1$, which means the system is bounded. We apply this technique successfully to a wide range of $\alpha$ in the $\lambda >0$ region. For $\lambda <0$, we found that the domain of $\alpha$ is limited to $\alpha \in [0,1.5]$, beyond this interval, the system collapsed, and the technique failed to give acceptable results.