Spectroscopy of the Dirac oscillator perturbed by a surface delta potential

Abstract

We study theoretically the level shift of the Dirac oscillator perturbed by any sharply peaked potential approaching a surface delta potential. A Green function method is used to obtain closed expressions for all partial waves and parities.

Figures (3)

• Figure 1: Energy levels of a Dirac oscillator perturbed by a surface delta potential as a function of the coupling constant $\lambda$ for $\omega=m$. Left and right panels correspond to $\kappa=-1$ and $\kappa=1$, respectively. Solid (dashed) lines correspond to the results for $R=0.3/m$ ($R=1/m$). The solutions of the unperturbed Dirac oscillator are marked with red points.
• Figure 2: Shift of the energy levels as a function of the radius $R$ for $\omega=m$, $\kappa=-1$ and $\lambda=\pi/4$. The levels of the unperturbed Dirac oscillator are plotted with dashed gray lines. The wave functions corresponding to the four red points are shown in Fig. \ref{['fig3']} The wave functions at points marked $a-d$ are shown in figure \ref{['fig3']} below.
• Figure 3: Plots of $|\bm \phi(r)|^2$ as a function of the dimensionless radial coordinate $z=r\cdot m$ for the four different values of the delta-shell radius $R$ indicated in figure \ref{['fig2']} by red circles, when $\omega=m$, $\kappa=-1$ and $\lambda=\pi/4$. The corresponding unperturbed eigenstate is plotted using gray solid regions.