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

Abstract 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 () =H₀- V H (α) = H 0 - α V in the interval (-1, 1) (- 1, 1) for large values of the coupling constant >0 α > 0. In particular, we obtain an asymptotic formula for the number of eigenvalues of H () H (α) situated in a bounded interval [, ) [ λ, μ) as α → ∞.