Physics 125a Midterm Solutions Due November 4, 2015
Problem 1
A quantum mechanical observable is represented by the Hermitian operator O. It has an orthonormal basis of eigenstates | , where O| = | .
Physics 125a Solutions of Problem Set 1
October 14, 2015
Problem 1
Let
u1 = (1, 1, 1, 1),
u2 = (1, 4, 4, 1),
u3 = (4, 2, 2, 0).
(1)
Then the orthogonal vectors are
v1 = u1 = (1, 1, 1, 1),
v1 u2
v2 = u
Physics 125a
Problem Set 3 Solutions
Problem 1
q
~
Using X = 2m
(a + a ) and P = i m~
(a a), along with a|ni = n|n 1i,
2
a |ni = n + 1|n + 1i, we see that
r
r
~
~
hXi = hn|X|ni =
hn|(a + a )|ni =
nhn
Ph125: Problem Set 1 Solutions
October 13, 2016
Problem 1
Note that,
|3i =
2 2
0 2
=2
0 0
1 0
+
2
2
2 2
= 2|1i + |2i .
Therefore, vector |3i is a linear combination of vectors |1i and |2i. This indica
Ph125a Homework 2 Solutions
Fall 2016
Problem 1
0 i are orthogonal states with unit norm, representing the particles K 0 and K
0 (these
|K 0 i and |K
particles are called neutral kaons). We approxim
0v
1; 034.5
/-
ll"
. ,mmmc
/ 0
0
W , L .
cfw_.M b .r. b
. . E
Q l . a K ,.
A , (a a _ c n _ w U. .
_._m In. , , _ /
AN. . , ,4 .
,Z_ A A, .w W: U _L :9 w
._ _ _ A m . m . _ . _
- 5 u H m I w m
Physics 125a Final Due Friday December 9, 2016
Instructions
You have up to three hours to do the exam once you start. You can use your notes, my notes on
the web, your problem sets (and solutions) and
Physics 125a Midterm Due November 2, 2016
Instructions
You have up to three hours to do the exam once you start. You can use your notes, my notes on
the web, your problem sets (and solutions) and the
Physics 125a
Problem Set 3, Due Wed. Nov 26, 2016
Problem 1
Find hXi, hP i, P and X for a particle of mass m in a one dimensional
harmonic oscillator, V (X) = (1/2)m 2 X 2 , in energy eigenstate |ni.
Physics 125a
Problem Set 3, Due Wed. Oct. 21, 2015
Problem 1
We are given the Hamiltonian H = g = g1 1 + g2 2 + g3 3 . The basis vectors of the Hilbert Space are |1 and
|2 which are eigenstates of 3 w
Ph125: Problem Set 5 Solutions
Chia-Hsien Shen
November 21, 2015
Problem 1
(a) The system is in the ground state of old SHO. The ground state is annihilated by its annihilation operator a,
a|0old = 0.
Lecture 15. Canonical Transformations
(Dated: November 17, 2015.)
I.
REVIEW FROM LAST TIME AND SUMMARY OF THIS LECTURE
Last time, we discussed:
1. Examples of converting the Lagrangian into Hamiltonia
Physics 125a
Problem Set 4, Due Wed. Nov. 11, 2015
Problem 1
Using X =
that
2m (a + a ) and P =
X = n|X|n =
2m
m
i
(a
2
a), along with a|n =
n|(a + a )|n =
2m
n|n 1 , a |n =
n n|n 1 +
n + 1 n|n + 1
Physics 125a
Problem Set 2, Due Wed. Oct. 14, 2015
Problem 1
|K 0 and |K 0 are two orthogonal states with unit norm that correspond to the particles K 0 and K 0 . These
particles decay into other part
Physics 125a
Problem Set 6, Due Wed. Nov 25, 2015
Problem 1
(a) Two identical bosons are found to be in the states | and . Write
down the normalized state vector describing the system when | =
0.
(b)
Physics 125a
Problem Set 4, Due Wed. Nov 9, 2015
Problem 1
A particle of mass m moves in one dimension under the influence of a harmonic oscillator potential
H=
P2
m 2 2
+
X
2m
2
(1)
The particle is i
Physics 125a
Problem Set 2, Due Wed. Oct. 12, 2016
Problem 1
|K 0 i and |K0 i are two orthogonal states with unit norm that correspond
to the particles K 0 and K0 . These particles decay into other pa
Physics 125a - Problem Set 1 - due October 5, 2016.
Problem 1 (5 points)
Consider three elements from the vector space (over the real numbers) of real 2 2 matrices,
0 0
2
2
2 2
, |2i =
, |3i =
(1)
|1i
Physics 125a
Problem Set 5, Due Wed. Nov 23, 2016
Problem 1
(a) Two identical bosons are found to be in the states |i and i. Write
down the normalized state vector describing the system when h|i 6=
0.