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