New class of exact solutions of the Dirac equation

Journal Article · Wed Jan 01 04:00:00 EST 1975 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.522424· OSTI ID:4145478

Felber, Franklin S.

A new class of exact solutions of the Dirac equation with external electromagnetic fields is derived by assuming a set of field-dependent solution matrices which obey an algebra isomorphic to the Pauli matrices. The method of exact solution may be applied to any field having a four-vector potential, A/sup $mu$/, depending only on k/sup $mu$/x/sub $mu$/, but for which the field tensor and initial electron momentum are such that A/sup $mu$/A/sub $mu$/, A/sup $mu$/ P/ sub $mu$/, (sigma/sup$mu$$nu$/F/sub$mu$$nu$/)$sup 2$, and (sigma/sup$mu$$nu$/ F'/ sub $mu$$nu$/)$sup 2$ are independent of k/sup $mu$/x/sub $mu$/. Exactsolutions for a circularly polarized propagating electromagnetic wave in an isotropic medium, for a screw-symmetric static magnetic field, and for a rotating uniform electric field are given in terms of the roots of a quartic equation. A class of solutions is given explicitly in the weak-field limit to lowest order in eA/ mc$sup 2$. The vacuum limit of the solution of a wave propagating in a medium is shown to be the Volkov solution.

• Research Organization: Univ. of California, Los Angeles
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-008611
• OSTI ID: 4145478
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 16; ISSN JMAPAQ; ISSN 0022-2488
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

*DIRAC EQUATION-- ANALYTICAL SOLUTION
644002*
ASYMPTOTIC SOLUTIONS
ELECTRIC FIELDS
ELECTROMAGNETIC FIELDS
ELECTROMAGNETIC RADIATION
MATRICES
N76100* --Physics (Theoretical)--General
POLARIZATION
TRAVELLING WAVES