Quantum harmonic oscillator coherent state interference

Here we visualize two coherent states of the quantum isotropic harmonic oscillator. A coherent state is a solution to Schödinger equation that behaves similarly to its classical counterpart. In this case, a classical point-like particle would move in an elliptical trajectory, so its quantum analogue does the same. However, due to Heisenberg's uncertainty principle, the state cannot be fully localized in phase space and therefore moves as a gaussian package. We introduce two packages moving in opposite directions. When two such packages with different phases (here, they differ by pi) meet, they interfere.
The domain is a square of side 10x10 and the packages orbit around a circle of radius 2.5. We have chosen Planck constant ħ=1, particle mass m=1 and oscillator frequency w=1 such that the characteristic scale of the packages is a=1. Any other choice leads to a simple reescaling. Colormap is proportional to the square root of the probability and saturated to half the maximum amplitude to highlight the small scale nature of the interference.
#physics #mathematics #simulation #numericalmethods #calculus #differentialequations #visualization #quantum #quantumphysics #interference

Видео Quantum harmonic oscillator coherent state interference канала FieldSolver