This simulation shows a Pauli spinor inside a hard-walled three-dimensional box, together with Bohmian particles guided by the Pauli current. The glowing cloud is the spinor density. The magnetic-field controls apply a uniform field along a selected axis and can start the spatial wave in low particle-in-a-box energy eigenstates.
Wave
The wave function is a two-component spinor. Its density is
The wave evolves according to the Pauli equation inside the box. All six faces are hard-walled, and particles are reflected back into the box if numerical stepping reaches a wall. The uniform field enters through the spin Zeeman term and through the symmetric-gauge vector potential in the kinetic term.
Guidance
The Bohmian velocity includes the Pauli current, the spin-current curl, and the magnetic vector potential term from A5. In simulation units the coupling is q/c = 1, with the symmetric-gauge vector potential about the box center.
The spin current uses the local Pauli spin density. The spin basis is spatially constant here, so the gradient of chi term in A5 vanishes.
Contours
The floor curves are level sets of the logarithmic density on the middle horizontal slice. Brightness follows the steepness of the logarithmic density.