Module log(10
12
) –
the rockin’ module
Getting Smarted
1.
A single particle hydrogenic wave function is expressed as
"
#
=
n
,
l
,
m
l
,
m
s
a.
What does it mean for two wave functions,
and
, to have the same spatial
wave functions?
b.
What does it mean for two wave functions,
and
, to have the same spin?
c.
If two electrons are distinguishable, how should we write their combined,
normalized twoparticle wave functions?
d.
For two single particle wave functions,
and
, that have the same spatial wave
functions and different spins, write the symmetric
combined, normalized wave
function,
.
e.
For two wave functions,
and
, with the same spatial wave functions and
different spins, write the antisymmetric
combined, normalized wave function,
.
f.
Correctly label your answers to c and d as either a fermion or boson.
g.
Why is the product of two singleparticle wave functions,
, satisfy the two
particle Schrödinger wave equation, but not represent a quantum system of fermions
or bosons? What system does this correctly model?
h.
Use symmetrization arguments to explain why fermions satisfy an exclusion
principle while bosons may form a BEC.
Disgusting Questions
1.
Three noninteracting muons are in a 1D box of length L. (Ignore their spin…for now.)
a.
What is the general form of the singleparticle wave function?
b.
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 Spring '09
 wave function, Slater

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