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>+=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.
Highlights
The of the wave particle plays important role in understanding of the behavourial description of particle as regards the electronic structure, energy spectrum and wave characteristics [1]
In this paper we have analytically studied the fundamental wave characteristics of free particle based on equation constructed from relativistically covariant wave equation of Schrodinger equation that satisfies Klein-Gordon equation
The expression for anticommutation relations that defined the algebraic matrices with special representation showing the diagonal matrices A, to AN in conjunction with the explicit representation of the Dirac matrices are seen in Equations (14a) and (14b) with their explicit value presented in Equations (15)-(18)
Summary
The of the wave particle plays important role in understanding of the behavourial description of particle as regards the electronic structure, energy spectrum and wave characteristics [1]. Many researchers probe into this using classical approach which was found to be insufficient in giving complete description particle. This is because relativistic effect which is of most important is in description of any physical system is excluded. Relativistic effect plays a crucial role the description of electronic structure of small particle and heavy particles [1]. In this work we intend to analyze the wave characteristics using relativistic approach by bringing together momentum relation, vectorial relation and Dirac wave in conjunction with Heisenberg representation observe in a real sense the feasibility of existence of single particle
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