Background: This problem refers back to Problem 3 of the previous problem set. It illustrates the power of physical concepts such as the conservation of probability.
Compute the probability current from your expression for
using the result from lecture
where 
is defined to be the imaginary part of the complex
number z.
Verify that your results satisfy
(
Background: Note that this verifies that the probability 
is conserved.)
Hint: The key to this problem is to stay organized and manage
your algebra. I suggest arranging things so that you can reuse
your result for 
from last lecture.