Dirac Systems with Discrete Spectra

Hinton, D. B. ; Shaw, J. K.

Canadian journal of mathematics, Tome 39 (1987) no. 1, pp. 100-122

Résumé

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.

Détail

DOI : 10.4153/CJM-1987-006-0

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