Spin-Dependent Bohm Trajectories for Pauli and Dirac Eigenstates of Hydrogen |
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Authors: | C Colijn E R Vrscay |
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Institution: | (1) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1 |
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Abstract: | The de Broglie-Bohm causal theory of quantum mechanics is applied to the hydrogen atom in the fully spin-dependent and relativistic framework of the Dirac equation, and in the nonrelativistic but spin-dependent framework of the Pauli equation. Eigenstates are chosen which are simultaneous eigenstates of the energy H, total angular momentum M, and z component of the total angular momentum M
z. We find the trajectories of the electron, and show that in these eigenstates, motion is circular about the z-axis, with constant angular velocity. We compute the rates of revolution for the ground (n=1) state and the n=2 states, and show that there is agreement in the relevant cases between the Dirac and Pauli results, and with earlier results on the Schrödinger equation. |
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Keywords: | de Broglie-Bohm theory Bohm trajectories causal interpretation of quantum mechanics relativistic quantum theory |
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