PHYS 234: Quantum Physics 1 (Fall 2008)
Assignment 5
Issued: October 10, 2008
Due: 12.00pm, October 17, 2008
1. Consider source atoms for a Stern Gerlach measurement which are in the state described by
1
=
6
1+i
2
(a) Calculate the respective probabilitie
Physics 202H - Introductory Quantum Physics I Homework #03 - Solutions Fall 2004 Due 5:01 PM, Monday 2004/10/04
[45 points total] Journal questions. Briey share your thoughts on the following questions: Considering your entire history as a student, what c
PH425 Spins Homework 2
Due 1/17/14
PRACTICE:
1. Quiz
1
A beam of spin- 2 particles is prepared in the state:
2
3
| = |+ + i |
13
13
(a) What are the possible results of a measurement of the spin component Sz , and
with what probabilities would they occur?
PHYS234 Quantum Physics 1 (Spring 2014)
Assignment 5
Issued: June 5th, 2014
Due: noon, June 12th, 2014
1. Consider source atoms for a Stern Gerlach measurement which are in the state described by
1
=
6
1+i
2
with respect to the z-basis cfw_ z , z
Note: t
PHYS234: Quantum Physics 1 (Spring 2014)
Assignment 4
Issued: May 29, 2014
Due: noon, June 5, 2014
1. Tutorial: From the tutorial on Quantum State Tomography, write up your computation for determining the quantum state of the source unknown 4 written as a
Solution set 2: Compton scattering
Compton scattering
1. Show that a photon cannot transfer all of its energy to a free electron.
(Hint: Energy and momentum must be conserved.)
Answer
The conservation of linear momentum implies,
h
= pe ,
(1)
whre pe is th
PHYS234 Practice Problems 8. For tutorials week of June
26; solutions June 28.
8.1
a) Show that the time-evolution of a density operator, , is determined by the equation,
d
1
= [H, ],
dt
i
h
(8.1)
where H is the Hamiltonian for the system.
b) Suppose tha
PHYS234 Practice Problems 2. For tutorials week of May
15; solutions May 19.
2.1
Eulers formula. a) Use the power series expansions for exponentials, sines, and cosines to
prove Eulers formula:
exp i = cos + i sin
(2.1)
b) Express cos and sin in terms of
PHYS234 Practice Problems 9. For tutorials week of July 3;
solutions July 7.
Note: For those of you impacted by the long weekend, seek assistance from the TAs or course
instructor directly or ask questions in tutorial the following week.
9.1
McIntyre Prob
PHYS234 Practice Problems 7. For tutorials week of June
19; solutions June 23.
7.1
McIntyre 3.16 (p96)
7.2
(Credit: Griffiths) An electron is at rest in an oscillating magnetic field,
B = B0 cos t
z
(7.1)
where B0 and are constants.
a) Construct the Hamil
PHY334 Practice Problems 1. For tutorials week of May 8:
solutions May 12.
1.1
The Bohr model for hydrogen. The magnitude of the attractive Coloumb force between
an electron and a proton is,
62 1
= 1.1
3.) Assume that the electron is in a circular orbit
PHYS234 Practice Problems 6. For tutorials week of June
12: solutions June 16.
6.1
McIntyre Problem 3.2 (p94)
6.2
McIntyre Problem 3.5 (p94)
6.3
McIntyre Problem 3.13 (p95)
6.4
McIntyre Problem 3.14 (p95)
6.5 Time-dependence with SPle
1] Calibrating the m
PHY5234 Practice Problems 2. For tutorials week of May
15: solutions May 19.
2.1
Eulers formula. 3.) Use the power series expansions for exponentials, sines, and cosines to
prove Eulers formula:
expi=cos+isin9 (2.1)
b) Express (3056 and sin in terms of co
PHYS234 Practice Problems 1. For tutorials week of May 8;
solutions May 12.
1.1
The Bohr model for hydrogen. The magnitude of the attractive Coloumb force between
an electron and a proton is,
|F| =
e2 1
,
40 r2
(1.1)
a) Assume that the electron is in a ci
PHYS234 Practice Problems 3. For tutorials week of May
22; solutions May 26.
Note: For those of you whose tutorials are impacted by the long weekend, bring your questions
to the tutorial the following week, seek assistance from your TA, or from the course
PHYS234 Practice Problems 10. For tutorials week of July
10; solutions July 14.
10.1
McIntyre Problem 6.2 p198 wavefunction iii) only. (Work on the others if you want extra
practice)
10.2
McIntyre p 6.4 p198.
10.3
(Credit: Griffiths) A free particle has t
PHYS234 Practice Problems 5. For tutorials week of June
5; solutions June 9.
5.1
Prove that Hermitian operators have real eigenvectors and, assuming no degeneracy, orthogonal eigenvectors.
a) Consider two eigenvectors of a Hermitian operator, A: A|1 i = a
PHYS234 Practice Problems 4. For tutorials week of May
29; solutions May 31.
Dont forget about the in-class test Friday June 2.
4.1
(modified from McIntyre) Consider the measurement arrangement shown in Fig 2.14 from
the textbook (p. 64, reproduced below)
Quantum Mechanics: A Paradigms Approach
David H. McIntyre
10 January 2014
Corrections to the 1st printing
page xxi, last paragraph before "The End", 2nd line: Change "become" to "became".
page 31, Problem 1.9, first line: Change "A pair of dice" to "Two d
PHYS234 Practice Problems 6. For tutorials week of June
12; solutions June 16.
6.1
McIntyre Problem 3.2 (p94)
6.2
McIntyre Problem 3.5 (p94)
6.3
McIntyre Problem 3.13 (p95)
6.4
McIntyre Problem 3.14 (p95)
6.5 Time-dependence with SPINs
1) Calibrating the
PHYS234 Practice Problems 12. For tutorials week of July
24; solutions July 26.
12.1
In class, we discussed scattering from the finite potential well. Fill in the steps in the derivation
of the ratios of the amplitudes,
F
ei2k1 a
=
k2 +k2
A
cos(2k2 a) i 2
PHYS234 Practice Problems 11. For tutorials week of July
17; solutions July 19.
11.1
McIntyre Problem 6.22 (p199)
11.2
McIntyre Problem 6.29 (p200)
11.3
(Credit: Griffiths) a) Write down the (time-dependent) Schrodinger equation in momentum
space for a fr