The Dirac Equation with the Scattered Electron Including Extra Potential Energy Comes from the Virial Theorem

Hasan Arslan

Physics Department, Bing?l University, Bing?l, Turkey.

DOI: 10.4236/jmp.2013.44078                

Abstract

The scattering of electron by a photon is a well-known reaction in physics. In this study, the change in the electron’s energy after the scattering is taken into account. The previous works are searched. In order to take into account this change in the electron’s energy in the equation of motion of the electron, the Dirac equation is used with the virial theorem. The scattered electron kinetic energy which is given to the electron by the loss in photon’s energy is related to the potential energy of the electron by the virial theorem which states that the potential energy is two times of the kinetic energy in minus sign. A first time application of the virial theorem on a scattered electron by a photon is included to the Dirac equation.

Keywords

Dirac Equation; Virial Theorem; Scattered Electron

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. Beiser, “Concepts of Modern Physics,” 4th Edition, McGraw-Hill International Editions, New York, 1987.
[2]	J. B. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1964.
[3]	J. J. Sakurai, “Advanced Quantum Mechanics,” Addison-Wesley, Menlopark, 1967.
[4]	J. B. Marion and S. T. Thornton, “Classical Mechanics of Particles and Systems,” 3rd Edition, Harcourt Brace Jovanovich, New York, 1988.
[5]	H. Goldstein, “Classical Mechanics,” Addison-Wesley Publishing Company, Inc., Boston, 1974.
[6]	M. Brack, “Virial Theorems for Relativistic Spin-1/2 and Spin-0 Particles,” Physical Review D, Vol. 27, No. 8, 1983, pp. 1950-1953. doi:10.1103/PhysRevD.27.1950
[7]	W. Greiner, S. Schramm and E. Stein, “Quantum Chromodynamics,” 2nd Edition, Springer-Verlag Berlin Heidelberg, Berlin, Heidelberg, 2002. doi:10.1007/978-3-662-04707-1