This recitation notebook is not due until OCT 5 !!!

This is a less structured recitation You will use the skills you have picked up last week to study the behavior of a wave-packet incident on a barrier. I highly recommend working together.

Work in units where $\hbar=m=1$ consider a box of length $L=40$, with hard wall boundary conditions. Use a grid spacing $dx=0.02$.

• Create a potential which is zero, except for between $x=20$ to $x=20.2$, where the potential has height $V_0=800$.
• Plot the potential.
• Create a Gaussian wavepacket centered at $x=4$ with wave-vector $k=12\pi$ and width $\delta x=1$
• Plot this wavepacket
• Use the tdseviewer package to animate the time evolution of this wavepacket. Use a timestep dt=0.0001, and integrate from time t=0 to time t=1. Plot only one frame out of 100. Store the time-series of the wavefunction.
• You should find that the wave-packet splits into two, with one part passing through the barrier, and the other reflecting.
• Analyze your stored time-series to calculate the probability that the wavepacket passes through the barrier.
• Repeat for barriers with thicknesses 0.4 and 0.8.
• Make a plot of the logarithm of the barrier penetration probability versus barrier thickness.