Spin-dependent Bohm trajectories for Pauli and Dirac eigenstates of hydrogen
نویسنده
چکیده
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 Mz. 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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Spin-dependent Bohm trajectories for hydrogen eigenstates
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