Dirac Equation
المؤلف:
Alvarez, A.; Pen-Yu, K.; and Vazquez, L
المصدر:
"The Numerical Study of a Nonlinear One-Dimensional Dirac Equation." Appl. Math. Comput. 18
الجزء والصفحة:
...
13-7-2018
3102
Dirac Equation
The quantum electrodynamical law which applies to spin-1/2 particles and is the relativistic generalization of the Schrödinger equation. In 
dimensions (three space dimensions and one time dimension), it is given by
 |
(1)
|
(Bjorken and Drell 1964, p. 6), where 
is h-bar, 
is the speed of light, 
is the wavefunction, 
is the mass of the particle, and 
are the Dirac matrices (with 
being called 
by Bjorken and Drell 1964, p. 8; Berestetskii et al. 1982, p. 78).
The Dirac equation can also be written in the concise form
 |
(2)
|
(Griffiths 1987, p. 216), where
 |
(3)
|
are Dirac matrices in the "Dirac basis" (Griffiths 1987, p. 216), and Einstein summation has been used to sum over 
, 1, 2, 3.
In 
dimensions, a generalization of the Dirac equation is given by the system of partial differential equations
(Alvarez et al. 1982; Zwillinger 1997, p. 137), where 
corresponds to the quantum electrodynamical equation.
REFERENCES:
Alvarez, A.; Pen-Yu, K.; and Vazquez, L. "The Numerical Study of a Nonlinear One-Dimensional Dirac Equation." Appl. Math. Comput. 18, 1-15, 1983.
Berestetskii, V. B.; Lifshitz, E. M.; and Pitaevskii, L. P. Quantum Electrodynamics, 2nd ed. Oxford, England: Pergamon Press, 1982.
Bethe, H. A. and Salpeter, E. Quantum Mechanics of One- and Two-Electron Atoms. New York: Plenum, p. 37, 1977.
Bjorken, J. D. and Drell, S. D. "The Dirac Equation." §1.3 in Relativistic Quantum Mechanics. New York: McGraw-Hill, pp. 6-9, 1964.
Dirac, P. A. M. "The Quantum Theory of the Electron." Proc. Roy. Soc. London A117, 610-624, 1928.
Dirac, P. A. M. "The Quantum Theory of the Electron, Part II." Proc. Roy. Soc. London A118, 351-361, 1928.
Dirac, P. A. M. Principles of Quantum Mechanics, 4th ed. Oxford, England: Oxford University Press, 1982.
Griffiths, D. J. "The Dirac Equation" and "Solutions to the Dirac Equation." §7.1-7.2 in Introduction to Elementary Particles. New York: Wiley, pp. 213-222, 1987.
Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 137, 1997.
الاكثر قراءة في المعادلات التفاضلية الجزئية
اخر الاخبار
اخبار العتبة العباسية المقدسة
