THE EQUIVALENCE OF CLASSICAL MECHANICS AND DIRAC THEORY IN SPIN–ORBIT INTERACTION ENERGY OF HYDROGEN ATOM By Dr. Motiur Rahman Ansari

Abstract

Some of the microscopic phenomena at atomic-nuclear level can be better understood with the help of famous Dirac Theory of Relativistic Quantum Mechanics. But for many of the research scholar levels, particularly in the research fields the transition from classical to relativistic quantum mechanics is abstract in understanding. This paper is an attempt to show how the two approaches lead to the same results and how beautifully explain the energy quantization at atomic level. The origin of the internal magnetic field experienced by an electron moving in a one electron atom is easy to understand if we consider the motion of the nucleus from the point of view of the electron. In a frame of reference fixed on the electron, the charged nucleus moves around the electron and the electron is in effect, located inside a current loop which produces the magnetic field. The author asserts with mathematical logic and relevant equations how the two treatments converge beautifully to one point in bringing the expression of quantized energy of the electron. We consider a semi-classical model to describe the origin of the spin-orbit interaction in a simple system such as the hydrogen atom.. The correct ½ factor for the spin-orbit coupling energy is thus derived without the need to invoke the well-known Thomas precession in the rest-frame of the electron. This result is in quality agreement with the solution of the Dirac-Coulomb equation for hydrogen atom. 

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