Physics 324, Fall 2001
Solutions to problem set #3
Fri. 10/26/01
2 problems chosen to be graded are marked by a and are worth 40 points each; the
tutorial questions are worth an additional 20 points total.
Gasiorowicz 2-12 Several ways to do this. Note th
Physics 324, Fall 2001
Solutions to problem set #4
Fri. 11/9/01
Problems chosen to be graded are marked by
(1) Gasiorowicz 4-4
We have x =
x2 x 2 Since all the un (x) are even or odd under x a x,
|un (x)|2 is always even under x a x, and so x = a/2. Then
Physics 324, Fall 2001
Solutions to problem set #5
Fri. 11/16/01
Problems chosen to be graded are marked by
(1)
a)
[AB, C] = AB C C AB
B C AC B + AC B C AB
= A
= A[B, C] + [A, C]B
(1)
b) Dene [, xn ] = [n , p] Cn . Then, using the result o
Altitudes and delay times will vary based on finished rocket weight.
Revised 4/28/15
4/29/2015
PLEASE READ THIS VERY IMPORTANT INFORMATION!
Data was produced from RockSim simulation software with 500' elevation launch site, 70% humidity, 75 deg. F, 0 mph
Problem Set 10
Physics 324A
Due Friday Dec. 7, 2012
Last problem set in 324!
1. Electron congurations
a) Using the alfbauprinzep, determine the electron congurations 1s2 2s2 . of Na, K, Mg,
Ca, Al, Ga, Ge, O, Ar and In.
b) Choose a favorite heavy atom in
Problem Set 9
Physics 324A
Due Friday Nov. 30, 2012
Note: Short set due to TG holiday last week.
1. Consider the possible angular momentum states |SM obtained by adding the angular
1
momenta of two s = 2 spins, i.e., S = s1 + s2 .
a) List the possible eig
Problem Set 8
Physics 324A
Due Monday Nov 26, 2012
Note: Due date is Monday Nov 26 due to holidays Nov 12 and 23 and exam Nov 16.
1. Verify that a) the spin operators satisfy the commutator relations [Sx , Sy ] = i Sz and
h
2
b) that the pauli matrices sa
Problem Set 7
Physics 324A
Due Friday Nov 9, 2012
Note: All Griths problems are from Introduction to Quantum Mechanics 2nd Edition.
1. Use separation of variables in cartesian coordinates to solve for the quantum states of
a particle of mass m in a square
Problem Set 6
Physics 324A
Due Monday Nov 2, 2012
Note: All Griths problems are from Introduction to Quantum Mechanics 2nd Edition.
1. a) Griths, Prob. 3.6.
b) The rotational kinetic energy K = 2 Q/2I here I is the moment of inertia. Determine
h
the eigen
Problem Set 5
Physics 324A
Due Friday Oct 26, 2012
Note: All Griths problems are from Introduction to Quantum Mechanics 2nd Edition.
1. Hermitian Operators in Quantum Mechanics
a) Griths, Prob. 3.4 (d)
b) Griths, Prob. 3.5 (b)
2. Momentum space wave funct
Problem Set 4
Physics 324A
Due Monday Oct 22, 2012
Note: All Griths problems are from Introduction to Quantum Mechanics 2nd Edition.
Note: Short set and changed due date due to Midterm Exam on Wed. Oct 17.
1. Simple harmonic oscillator (SHO) properties
a)
Problem Set 3
Physics 324A
Due Friday Oct 12, 2012
Note: All Griths problems are from Introduction to Quantum Mechanics 2nd Edition.
1. Consider the integrals Hmn = dx m H (, x)n , and Smn = dx m n , where H =
p
p2 /2m + V (x) and cfw_n are eigenstates o
Physics 324, Fall 2001
Solutions to problem set #1
Fri. 10/12/01
Problems chosen to be graded are marked by
(1) Gasiorowics 1-2
Integrating eq. (1-1) over gives U (T ) = 4 E(T ). Combining with
c
eq. (1-12a) then yields E(T ) = ca T 4 T 4 . Plugging in nu
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Physics 324, Fall 2001
Problem set #4
Due: Fri. 11/9/01
Assigned problems. All four are to be turned in; problem (3) and one other will be graded
and will be worth 50 points each.
1. Gasiorowicz, Ch. 4, #4
2. Gasiorowicz, Ch. 4, #6
? 3. Consider a particl
Physics 324, Fall 2001
Problem set #1
Due: Fri. 10/12/01
Assigned problems. All are to be turned in; four of the problems (the last
problem, plus three others chosen at random) will be graded, and will be worth
25 points each.
1. Gasiorowicz, Ch. 1, #2
2.
Appearance of photographic film after a short period of time with:
low intensity light.
a low intensity beam of electrons.
Appearance of photographic film after a long period of time with electrons incident on two slits
Handout 1
Physics 324, Fall 2001
Problem set #3
Due: Fri. 10/26/01
Assigned problems. All four are to be turned in; two will be graded and will be worth 50
points each.
1. Gasiorowicz, Ch. 2, #12
2. Gasiorowicz, Ch. 3, #6
3. Gasiorowicz, Ch. 3, #8
4. Gasiorowicz, C
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Physics 324, Fall 2001
Problem set #2
Due: Fri. 10/19/01
Assigned problems. All four are to be turned in; two will be graded and will be worth 50
points each.
1.
a) Consider a particle of mass m conned to a very thin wire of length L; you can
treat this a
Problem Set 2
Physics 324A
Due Friday Oct 5, 2012
1. Suppose that the wave function for a particle in a particular one-dimensional system at
2
t = 0 is given by (x, 0) = Ae(1/2)(xa) eikx
a) Determine the current density J (x, t) = Re (x, t) (/m) (x, t), w
Problem Set 1
Physics 324A
Due Friday Sep 28, 2012
Note: Very short problem set for rst week.
1. Suppose that the wave function for a particle in a particular one-dimensional system is
given by (x) = A exp(|x x0 |/a). The quantum mechanical probability de
PHYS 331: Optics Laboratory
Professor: Xiaodong Xu
Department: Physics
Propagation of Uncertainty Notes
Propagation of uncertainty: a.k.a. casually error propagation, the method of
computing the uncertainty in a result which depends on several variables,