Showing papers by "Don B. Hinton published in 1987"

Dirac systems with discrete spectra

Abstract: In this paper we consider the one dimensional Dirac system 1.1 where αk(x) < 0, λ is a complex spectral parameter, and the remaining coefficients are suitably smooth and real valued. We regard (1.1) as regular at x = a but singular at x = b; in Section 4 we extend our result to problems having two singular endpoints. Equation (1.1) arises from the three dimensional Dirac equation with spherically symmetric potential, following a separation of variables. For the choices p(x) = k/x, αk(x) = 1,p 2(x) = (z/x) + c, p 1(x) = (z/x) – c, and appropriate values of the constants, (1.1) is the radial wave equation in relativistic quantum mechanics for a particle in a field of potential V = z/x [17]. Such an equation was studied by Kalf [11] in the context of limit point-limit circle criteria, which is one of the matters we consider here.

Boundary conditions for differential operators with intermediate deficiency index

Abstract: The problem of assigning boundary conditions at singular endpoints is considered for differential operators which are neither limit-point or limit-circle at the singular endpoint. A solution is obtained by using Niessen subspaces. Additional asymptotic information yields a concrete description of the boundary conditions including a characterization of the Friedrich's extension.