Ph 129a
Problem Set 4
Due: Nov. 7, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) Show explicitly that the dening matrices of SO(1,1) give a reducible re
Ph 129a
Problem Set 6
Due: Nov. 21, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) By generalizing the construction in the last problem of the previous p
Ph 129a
Problem Set 7
Due: Dec. 3, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) In class we showed that the rotational SO(3) symmetry of the Bohr atom
Physics 129A, Fall 2013
Problem set 1 Solution
Shu-Ping Lee, Chan Y. Park
Problem 1
Which of the following dene groups? For those that do not, indicate the reason why:
(a) The set of all complex n n m
Physics 129A, Fall 2013
Problem Set 3 Solutions
Shu-Ping Lee
Problem 1. Irreducible representations of cyclic group
By Schurs rst lemma, every complex irreducible representation of Abelian groups is o
Physics 129A, Fall 2013
Problem Set 2 Solution
H.-J. Chung
Problem 1
Given that H is a subgroup of G and N is a normal subgroup of G, prove that N H is a normal
subgroup of H.
Solution (revised by Cha
Physics 129A, Fall 2013
Problem Set 4 Solutions
H.-J. Chung
Problem 1
Show explicitly that the dening matrices of SO(1, 1) give a reducible representation of the group
and that SO(1, 1) is isomorphic
Physics 129A, Fall 2013
Problem Set 5 Solutions
Shu-Ping Lee, Chan Y. Park
Problem 1.
Solution (Shu-Ping Lee):
z1
z2
ej (
m
j+m jm
z 1 z2
)=
(1)
(j + m)!(j m)!
If g is an element of SU(2), then g = ex
Physics 129A, Fall 2013
Problem Set 6 Solution
H.-J. Chung, Chan Y. Park
Problem 1
By generalizing the construction in the last problem of the previous problem set to the complex
case, construct the g
Ph 129a
Problem Set 5
Due: Nov. 14, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) Recall that the spin j UIR of SU (2), D(j) (g), was constructed in cla
Ph 129a
Problem Set 3
Due: Oct. 31, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of LauritsenDowns.
1) Construct all the irreducible representations of the cyclic group
Ph129 HW1 solution:
Problem 1:
for t > 0:
There is one pole ( = E i) located inside contour CR1
Figure 1. contour CR1
Let = Rei , R
(1)
eit
d
<
E + i 2
CR1
0
eRtsin()
Rd = 2
RE
/2
0
eRtsin()
Rd < 2
Physics 129A, Fall 2010
Problem Set 2 Solution
H. -J. Chung
October 17, 2010
1. Convolution theorem
Let Fcfw_f (k ), Fcfw_g (k ) be the Fourier transform of functions f (x), g (x), respectively. Then
Physics 129A, Fall 2010
Problem Set 3 Solution
Shu-Ping Lee
October 31, 2010
Problem 1:
xt
= (x, t)ln(x)
t
x
(1)
(x0 , t) = (x(x0 ,t) , t)
(2)
dx(x0 ,t)
d
=
+
=
(xt) +
dt
x dt
t
x
t
(3)
dx(x0 ,t)
=
Physics 129A, Fall 2010
Problem Set 4 Solution
H. -J. Chung
November 4, 2010
1. The eld of a tip
(a)
We put a metallic wedge of angle and take conformal mapping z = w 2 as in gure (1). The
positive re
Physics 129A, Fall 2010
Problem set 5 Solution
Shu-Ping Lee
November 17, 2010
Problem 1. Bcklund transformations
a
(a)
vx = ux + 2ae(u+v)/2
(3)
1
1
vxy = uxy + e(uv)/2 (ux vx )
a
2
x
(2)
1
vy = uy + e
1
Ph 129 Mid-term
1. Dissipative string. Consider the modied wave equation for the displacement of a string:
2
2
+ 2
+ 2
= 0.
t2
t
x2
(1)
with > 0.
(a) What is the Green function, G(x, t) of this eq
Ph 129a
Problem Set 2
Due: Oct. 24, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) Given that H is a subgroup of G and N is a normal subgroup of G, prove
Ph 129a
Problem Set 1
Due: Oct. 17, 2013
Please put your solutions in Hee-Joong Chungs mailbox on the fourth oor of Lauritsen.
1) Which of the following dene groups? For those that do not, indicate th
Physics 129A, Fall 2013
Problem Set 7 Solution
H.-J. Chung, Chan Y. Park
Problem 1
Solution (Chan Y. Park):
When we consider an n n matrix O in the dening representation of SO(n), we act this on pi
an