WarmUp Exercise #9, 9/21  (Assignment Due 9/23)

1. Calculate the probability current density, J(x) = (hbar/2mi)[ψ*(dψ/dx) - (dψ*/dx)ψ], for the following wave functions:
   1. ψ(x,t) = A e^i(kx-ωt)
   2. ψ(x,t) = A e^-i(kx+ωt)
   3. ψ(x,t) = A e^κx-iωt
   4. ψ(x,t) = A e^-κx-iωt

2. The animation below depicts a 1-d scattering process.  You can click-drag (up or down) in the animation to change the energy of the incident plane wave (up or down).  How do you think the analysis you just did for the probability current density relates to the various situations depicted in the animation below?

Answer in the form below, a short answer for each is fine. 
This report is due by 8:00 am Thursday morning.