Spectral analysis of one-dimensional Dirac operators with slowly decreasing potentials (Q1424738)

Here, Dirac systems \(H(\alpha)\), \[ H(\alpha)u=\left(\begin{matrix} 0 & -1 \\ -1 & 0 \end{matrix} \right) u' + \left(\begin{matrix} p_1 & q \\ q & p_2 \end{matrix}\right)u \] on the half axis \((0,\infty)\) for a vector function \((u_1,u_2)^{ t}\) with the boundary condition \(u_1(0)\cos \alpha + u_2(0) \sin\alpha=0\) with square integrable potential, are studied. The author shows that the absolutely continuous spectrum of \(H(\alpha)\) covers the whole real line. For Coulomb-like potentials, it is shown that \(H(\alpha)\) has at most \(4C^2\) distinct eigenvalues, where \(C=\limsup_{x\to\infty} x | V(x)| \).