On the Number of Eigenvalues of the Dirac Operator in a Bounded Interval

Let \(H_0\) $H_0$ be the free Dirac operator and \(V \geqslant 0\) $V⩾0$ be a positive potential. We study the discrete spectrum of \(H(\alpha )=H_0-\alpha V\) $H(\alpha )=H_0-\alpha V$ in the interval \((-1,1)\) $(-1,1)$ for large values of the coupling constant \(\alpha >0\) $\alpha >0$ . In particular, we obtain an asymptotic formula for the number of eigenvalues of \(H(\alpha )\) $H(\alpha )$ situated in a bounded interval \([\lambda ,\mu )\) $[\lambda ,\mu )$ as \(\alpha \rightarrow \infty \) $\alpha \to \infty$ .