arXiv subjects

C. Colijn

Publications and source records attributed to C. Colijn.

3 recordsLinked to original sources

arXiv2003

Spin-dependent Bohm trajectories for hydrogen eigenstates

The Bohm trajectories for several hydrogen atom eigenstates are determined, taking into account the additional momentum term that arises from the Pauli current. Unlike the original Bohmian result, the spin-dependent term yields nonstationary trajectories. The relationship between the trajectories and the standard visualizations of orbitals is discussed. The trajectories for a model problem that simulates a 1s-2p transition in hydrogen are also examined.

quant-ph↗

arXiv2003

Spin-dependent Bohm trajectories associated with an electronic transition in hydrogen

The Bohm causal theory of quantum mechanics with spin-dependence is used to determine electron trajectories when a hydrogen atom is subjected to (semi-classical) radiation. The transition between the 1s ground state and the 2p0 state is examined. It is found that transitions can be identified along Bohm trajectories. The trajectories lie on invariant hyperboloid surfaces of revolution in R^3. The energy along the trajectories is also discussed in relation to the hydrogen energy eigenvalues.

quant-ph↗

arXiv2003

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

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.

quant-ph↗