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

中文翻译：

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关于有界区间内狄拉克算子的特征值个数

设\(H_0\)为自由狄拉克算子，\(V \geqslant 0\)为正势。我们研究耦合常数\(\alpha >0\)较大值时区间\((-1,1)\)中\(H(\alpha )=H_0-\alpha V\)的离散谱。特别地，我们获得位于有界区间\([\lambda ,\mu )\)内的\(H(\alpha )\)特征值个数的渐近公式为\(\alpha \rightarrow \infty \)。