Spin-dependent Bohm trajectories for Pauli and Dirac eigenstates of hydrogen

Details Spin-dependent Bohm trajectories for Pauli and Dirac eigenstates of hydrogen Spin-dependent Bohm trajectories for Pauli and Dirac eigenstates of hydrogen

2003-04-29

arxiv.org/abs/quant-ph/0304198v1

Found. Phys. Lett. Vol. 16, No. 4 pp. 303-323 (2003)

Physics

Quantum Physics

15 pages

Scientific paper

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 Schrodinger equation.

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