The generalized relativistic harmonic oscillator with a point interaction

We study the perturbation of the one-dimensional generalized relativistic harmonic oscillator (GRHO) by a Lorentz scalar delta-shaped interaction. By exactly solving the implied Dirac equation, we show that the presence of the singular potential brings about drastic changes in the structure of the energy spectrum of the system. Particularly, an apparent anomaly of doubly degenerate energy levels is noted when the strength of the local term becomes infinite and energy eigenvalues in the range [Formula: see text] are obtained for some negative values of the delta-coupling and for all settings of the oscillator parameters.