- #1
CAF123
Gold Member
- 2,948
- 88
Homework Statement
Let V(x) = +∞ for x ≤ 0, -V1 for 0 < x < b and 0 for x > b. V1 and b are positive. The solutions in each of the physical regions are ##\psi_1 = P \exp(ik_1 x) + Q \exp (-ik_1 x)## and ##\psi_2 = R \sin (k_2x + \gamma)##.
Show that ##\lim_{V_1 \rightarrow 0} \gamma = 0##
The Attempt at a Solution
I am trying first to understand what ##\gamma## actually represents. I know to obtain the solution in region 2, it is a phase shift constant and so that solution is equivalent to a LC of sin and cos solutions. I also derived a relation between ##k_1, k_2 ##and ##\gamma## using the continuity conditions, but I am not sure how (or if) to apply it here.
Any hints in the right direction would be great.
Thanks.