Simple Chaotic Motion of Quantum Particles According to the Causal Interpretation of Quantum Theory

time steps

0

phase α

0.5

phase β

3.14159

The causal interpretation of quantum theory developed by David Bohm introduced trajectories that are guided by a real phase function

S

from the wavefunction in the polar form. A simple model is used to get chaotic motion; the trajectories undergo a transition from order to chaos depending on the relative phase factors

α

and

β

. The trajectories circle close to the minimum (nodal) points. For example, at the origin the squared wavefunction has a minimum for all

t

:

Ψ(0,0,t)

*

Ψ

(0,0,t)=

1

2

a

. The graphic shows the squared time-dependent wavefunction, the quantum particles, and the complete paths.