Physics – General Physics
Scientific paper
2007-07-17
Physics
General Physics
12 pages, v6: Accepted for publication in Pramana - J. Phys. with revisions and extension to quarkonium physics
Scientific paper
A non-perturbative relativistic atomic theory is presented. Spin is successfully introduced in Schrodinger dynamics of particle motion and the resulting energy levels of Hydrogen atom are shown to be exactly same as that of Dirac's theory. The separation of new radial and angular wave equations in spherical polar coordinates is as simple as that of the Schrodinger theory. The solutions of the angular part of the wave equation for spin 0 particle are exactly same as that of the Schrodinger theory. The spherical harmonics for spin 1/2 particle are same as in Dirac's theory. The radial wave function of the Schrodinger theory gets split into two spinor components. The new theory accounts for the energy due to spin-orbit interaction as well as for the additional potential energy due to spin and spin-orbit coupling. Spin angular momentum operator is as neatly integrated into the equation of motion as the orbital angular momentum operator. This requires modification to classical Laplacian operator. Consequently the Dirac matrices and the k operator of Dirac's theory are dispensed with. The theory also points out that the curvature of the orbit draws on certain amount of kinetic and potential energies affecting the momentum of electron and the spin-orbit interaction energy constitutes a part of this energy. It is shown that the correction introduced to the radial equation due to the modification of classical Laplacian is not the same as that of the Darwin and Pauli theroy however, the resulting energy levels of Hydrogen atom are same as that of Darwin, Pauli and Dirac theories. This is because the new theory is not a perturbation theory. Probability current density for Hydrogen atom and for free particle is discussed. The Pauli equation is obtained in the non relativistic limit.
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