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Villalba, Víctor M.

Separation of variables and exact solution to the Dirac equation in curvilinear orthogonal coordinates with cylindrical symmetry. (English) Zbl 0726.58067

J. Math. Phys. 31, No. 11, 2702-2707 (1990).
Summary: A complete separation of variables in the Dirac equation for a free particle is achieved in parabolic cylinder and elliptical coordinates. The resulting system of ordinary differential equations is solved and the asymptotic behavior of the spinor solutions is discussed.

MSC:

58Z05 Applications of global analysis to the sciences
35Q40 PDEs in connection with quantum mechanics
81T10 Model quantum field theories

Keywords:

curvilinear coordinates; orthogonal transformations; symmetry; cylindrical configuration; charged particles; elliptical configuration; asymptotic solutions; spinors; separation of variables; Dirac equation; ordinary differential equations
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References:

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