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Physics 401  Homework #11
1)
A spherical harmonic (three points)
. Apply the definition of the spherical harmonics
to calculate the explicit functional form for Y
3
1
(
The definition is given, for example,
in Griffiths, equations 4.27, 4.28, and 4.32.
2)
L
x
eigenstates
.
L
x
and L
z
do not have eigenstates in common, because their operators
do not commute. However, we can find eigenstates of L
x
which are linear combinations
of the eigenstates of L
z
.
a) (three point) Determine an expression for the (L
x
) operator in terms of the
ladder operators (L
+
) and (L

) (Lplus and Lminus).
b) (three points) Show that the following combinations of angular momentum
states are eigenstates of L
x
, and identify their eigenvalues. Hint: use the form of the L
x
operator determined in part (a).
1
,
1
0
,
1
2
1
,
1
2
1
3
1
,
1
1
,
1
2
1
2
1
,
1
0
,
1
2
1
,
1
2
1
1
state
Lx
state
Lx
state
Lx
c) (three points) Suppose that a particle is in the eigenstate "Lxstate2", defined
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This note was uploaded on 12/29/2011 for the course PHYSICS 401 taught by Professor Hall during the Fall '11 term at Maryland.
 Fall '11
 HALL
 Work, Quantum Physics

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