Investigating the reflectionless potential using the split-step algorithm

The reflectionless potential has the following functional form: \begin{equation} V(x) = -\frac{\hbar^2a^2}{m}sech^2(ax) \end{equation}

By comparing the propagation of a Gaussian wavepacket in this reflectionless potential to a similar strength and width square well, this unique behaviour can be observed.

For an explaination of the split-step method see the previous notebook

In [1]:
#NAME: Reflectionless Potential (1D)
#DESCRIPTION: Investigating the reflectionless potential in 1D using the split-step algorithm.

import pycav.display as display

Example Animation

In [2]:
display.display_animation('reflectionless.mp4')
Out[2]:
In [19]:
display.display_animation('reflection.mp4')
Out[19]: