Analysis of Characteristic of Free Particles: Relativistic Concept

Affiliation(s)

Departments of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria.

Departments of Computer Science, Ebonyi State University, Abakaliki, Nigeria.

Departments of Industrial Physics, Ebonyi State University, Abakaliki, Nigeria.

Departments of Computer Science, Ebonyi State University, Abakaliki, Nigeria.

ABSTRACT

A linear Hamiltonian in spatial derivative that satisfies Klein-Gordon equation was used starting from energy momentum relation for free particle was solved in agreement with the matrices and bearing in mind their suitability in terms of anticommutation relations in parallel with the definition of algebraic matrices whose hermicity is fulfilled by_{i} ^{+}= _{i} and ^{+}= and in turn linked up to explicit representation of the Dirac matrices. The wave packets of plane Dirac wave obtained as a superposition of plane wave yielding a localized wave function was normalized considering only positive energy of plane wave in which the expectation value with respect to the wave packet resulted from 2p/E>_{+}=<(v_{gr})> was found to agree with the Ehrenfest theorem in relation to Schrodinger theorem as it relates to true velocity of single particle. A comparison was made between the classical concept with Heisenberg representation from where the combined effect of the positive and negative energy components was considered.

A linear Hamiltonian in spatial derivative that satisfies Klein-Gordon equation was used starting from energy momentum relation for free particle was solved in agreement with the matrices and bearing in mind their suitability in terms of anticommutation relations in parallel with the definition of algebraic matrices whose hermicity is fulfilled by

Cite this paper

E. Ugwu, D. Onah, D. Oboma and V. Eke, "Analysis of Characteristic of Free Particles: Relativistic Concept,"*Journal of Modern Physics*, Vol. 3 No. 10, 2012, pp. 1394-1397. doi: 10.4236/jmp.2012.310176.

E. Ugwu, D. Onah, D. Oboma and V. Eke, "Analysis of Characteristic of Free Particles: Relativistic Concept,"

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[1] A. L. A. Fonseca, D. L. Nascimento, F. F. Monteiro and M. A. Amato, “A Variational Approach for Numerically Solving the Two-Component Radial Dirac Equation for One-Particle Systems,” Journal of Modern Physics, Vol. No. 4, 2012, pp. 350-354.

[2] R. Franke, “Numerical Study of the iterated solution of one electron Dirac Equation based on ‘Dirac Perturbation theory’,” Chemical Physics Letters, Vol. 264, No. 5, 1997 pp. 495-501. doi:10.1016/S0009-2614(96)01361-9

[3] S. McConnel, S. Fritzsch and A. Surzhykoy, “Dirac: A New Version of Computer Algebra Tools for Studying the Properties and Behaviour of Hydrogen-Like Ions,” Computer Physics Communication, Vol. 181, No. 3, 2010, pp. 711-713.

[4] A. Surzhykoy, P. Koval and S. Fritzsch, “Algebraic Tools for Dealing with Atomc Shell Model. 1. Wavefunctions and Itegrals for Hydrogen-Like Ions,” Computer Physics Communication, Vol. 165, No. 2, 2005, pp. 139-156. doi:10.1016/j.cpc.2004.09.004

[5] A. Zee, “Quantum Field Theory in Nutshell,” Princeton University Press, Princeton, 2010.

[6] P. W. Atkins, “Molecular Quantum Mechanics,” Oxford University Press, Oxford, 1983.

[7] R. A. C. Dirac, “The Lagrangian in Quantum Mechanics,” Physikalisch Zeitchrift der Sowjetunion, Vol. 3, 1933, pp. 62-72.

[8] R. Ballan and J. Zinn-Justin, “Methods in Field Theory,” North Holland Publishing, Amsterdam and World Scientific, Singapore City, 1981.

[9] P. A. M Dirac, “Principle of Quantum Mechanics,” Oxford University Press, Oxford, 1935.

[10] E. G. Milewski, “Vector Analysis Problem Solver,” Research and Education Association, New York, 1987.

[11] L. H. Ryder, “Quantum Field Theory,” Cambridge University Press Cambridge, 1996.