This preview shows page 1. Sign up to view the full content.
1
Problem set 6  Sharp potentials
Due on Wednesday, October 25, 2011. Posted on Oct. 19
1. To the edge of the cliﬀ and back
. In classical mechanics a particle hitting the a wall (i.e. a potential jump) gets
reﬂected. In quantum mechanics, a particle will also get reﬂected from a potential drop. Consider an electron
moving with momentum
p
= ¯
hk
from
x
=
∞
towards a drop described by the following potential landscape:
V
(
x
) =
{
0
x <
0

V
0
x >
0
V
0
>
0
(1)
(a) Find the timeindependent wave function describing the electron (assume the incoming amplitude is 1).
What is the amplitude of the reﬂected wave, and of the transmitted wave? Give your answers in terms of
p, V
0
and any constants associated with electrons.
(b) What are the reﬂection and transmission
probabilities
? How does the transmission probability behave as
V
0
→ ∞
?
(c) What are the reﬂection and transmission probabilities for an electron moving with group velocity
v
=
10
6
m/s
scattering oﬀ a potential drop of
V
0
= 30
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 03/21/2012 for the course PH 357 taught by Professor Tamiperegbarnea during the Fall '10 term at McGill.
 Fall '10
 TamiPeregBarnea
 mechanics, Work

Click to edit the document details