Uploaded September 2021 | Updated September 2026, 2 weeks ago
Music by @gpcbass! The song is called End of 9.
Releasing an off-centered Gaussian wave packet, being a superposition of eigenstates, in a quantum harmonic oscillator potential, i.e., a parabola, yields oscillations back and forth, where the wave packet retains its initial shape at the turning points.
The same does not apply for other soft potentials such as, e.g., an upside-down Gaussian potential in which the off-centered Gaussian wave packet disperses over time.
The time evolution considered in the first part is analytically solvable. Here it's done numerically though.
Done in Python and FFmpeg.
Music by @gpcbass! The song is called End of 9.
Releasing an off-centered Gaussian wave packet, being a superposition of eigenstates, in a quantum harmonic oscillator potential, i.e., a parabola, yields oscillations back and forth, where the wave packet retains its initial shape at the turning points.
The same does not apply for other soft potentials such as, e.g., an upside-down Gaussian potential in which the off-centered Gaussian wave packet disperses over time.
The time evolution considered in the first part is analytically solvable. Here it's done numerically though.
Done in Python and FFmpeg.
