Chin. Phys. Lett.  2010, Vol. 27 Issue (8): 084703    DOI: 10.1088/0256-307X/27/8/084703
FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
On the Generalized Continuity Equation

Arbab I. Arbab1, Hisham. M. Widatallah2

1Department of Physics, Faculty of Science, University of Khartoum, PO Box 321, Khartoum 11115, Sudan 2Department of Physics, College of Science, Sultan Qaboos University, PO Box 36 Al-Khod, Muscat 123, Oman
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Arbab I. Arbab, Hisham. M. Widatallah 2010 Chin. Phys. Lett. 27 084703
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Abstract

A generalized continuity equation extending the ordinary continuity equation is found using quanternions to show it is compatible with Dirac, Schrödinger, Klein-Gordon and diffusion equations. This generalized equation is Lorentz invariant. The transport properties of electrons are found to be governed by the Schrödinger-like equation and not by the diffusion equation.

Keywords: 47.10.A-      47.75.+f      47.90.+a      47.10.-g     
Received: 09 November 2009      Published: 28 July 2010
PACS:  47.10.A- (Mathematical formulations)  
  47.75.+f (Relativistic fluid dynamics)  
  47.90.+a (Other topics in fluid dynamics)  
  47.10.-g (General theory in fluid dynamics)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/27/8/084703       OR      https://cpl.iphy.ac.cn/Y2010/V27/I8/084703
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Arbab I. Arbab
Hisham. M. Widatallah
[1] Arbab A I and Satti Z A 2009 Prog. Phys. 8 2
[2] Hamilton W R 1844 Philosophical Magazine 25 489
[3] Tait P G 1873 An Elementary Treatise on Quaternions 2nd edn (Cambridge: Cambridge University)
Kelland P and Tait P G 1904 Introduction to Quaternions 3rd edn (London: Macmillan)
[4] Jackson J D 1975 Classical Electrodynamics 2nd edn (New York: John Wiley)
[5] Drude P 1900 Annalen der Physik 306 566
[6] Bjorken J D and Drell S D 1964 Relativistic Quantum Mechanics (New York: McGraw-Hill)
[7] Lawden D F 1968 Tensor Calculus and Relativity (London: Methuen)
[8] Arbab A I 2009 14th International Conference on Modelling Fluid Flow (CMFF'09) (Budapest, Hungary 9-12 September 2009)
[9] Fick A 1855 Ann. Phys. (Leipzig) 170 59
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