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

Let H₀ H 0 be the free Dirac operator and V 0 V ⩾ 0 be a positive potential. We study the discrete spectrum of H(α )=H₀-α V H ( α ) = H 0 - α V in the interval $$(-1,1)$$ ( - 1 , 1 ) for large values of the coupling constant α >0 α > 0 . In particular, we obtain an asymptotic formula for the number of eigenvalues of H(α ) H ( α ) situated in a bounded interval [λ ,μ ) [ λ , μ ) as α → ∞ α → ∞ .