3D Quantum Trajectory for a Particle in a Harmonic Potential

ω

x

0.5

ω

y

0.4

ω

z

0.6

time steps

100

initial positions

x

0

0.8

y

0

0.6

z

0

0.9

viewing angle

0.2

The quantum harmonic oscillator is an example of a nondispersive Gaussian wave packet that oscillates harmonically and is centered around



r

=

a

at

t=0

. This Demonstration shows the motion of a 3D quantum particle, which could be described by three harmonic oscillators in three-dimensional configuration space (CS). In this case, the independence of the orthogonal motions of the oscillator is assured. Independence of the component motions is maintained if the wavefunction is factorizable in CS.

If factorizability of the wavefunction is not possible, for example because of quantum superposition represented by a product state, the motion becomes entangled, meaning that the motion in one coordinate direction depends on other coordinate directions. If the CS is defined as real space, entanglement is equivalent to quantum nonlocality. Thus in the Bohmian approach, nonlocality is associated with nonfactorizability of the wavefunction.

The graphic shows the squared wavefunction and the trajectory.