This preview shows pages 1–2. Sign up to view the full content.
PHYS 385 Lecture 11  Bound states of a square well
11  1
©2003 by David Boal, Simon Fraser University.
All rights reserved; further copying or resale is strictly prohibited.
Lecture 11  Bound states of a square well
What's important
:
•
bound states in 1D square well
•
minimal conditions for binding
•
examples
Text
: Gasiorowicz, Chap. 5
Bound states of a square well
In the previous lecture, we determined the
unbound
states of a square well potential in
one dimension.
E
= 0

V
o
2
a
By
unbound
, we mean that
E
> 0, so the object can escape to infinity.
But there may
also be bound states (where
E
< 0), although their existence depends on the nature of
the well: the width and depth of the well must satisfy a constraint in order for bound
states to exist.
In addition, there are a finite number of bound states for a finite well
(unlike the Coulomb potential, as we saw in the Bohr model for hydrogenlike atoms).
As before, the candidate wavefunctions are exp(
iqx
) because
V
(
x
) is locally constant
except at the boundaries 
x
 =
a
.
Outside of the boundaries, 
x
 >
a
, the wavefunctions
are still exponentials, but the combination
2
mE
/
h
2
is complex because
E
< 0.
Thus, the function exp(
ikx
) is pure real for pure imaginary
k
,
and may grow or decay with
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 09/07/2009 for the course PHYS 385 taught by Professor Davidboal during the Spring '09 term at Simon Fraser.
 Spring '09
 DavidBoal
 Quantum Physics

Click to edit the document details