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Course schedule

(Preliminary schedule -- subject to frequent adjustment.)
DateF&W ReadingTopic Assignment
1 Wed, 8/29/2012Chap. 1 Review of basic principles;Scattering theory #1
2 Fri, 8/31/2012Chap. 1 Scattering theory continued #2
3 Mon, 9/03/2012Chap. 1 Scattering theory continued #3
4 Wed, 9/05/2012Chap. 1 & 2 Scattering theory/Accelerated coordinate frame #4
5 Fri, 9/07/2012Chap. 2 Accelerated coordinate frame #5
6 Mon, 9/10/2012Chap. 3 Calculus of Variation #6
7 Wed, 9/12/2012Chap. 3 Calculus of Variation continued
8 Fri, 9/14/2012Chap. 3 Lagrangian #7
9 Mon, 9/17/2012Chap. 3 & 6 Lagrangian #8
10 Wed, 9/19/2012Chap. 3 & 6 Lagrangian #9
11 Fri, 9/21/2012Chap. 3 & 6 Lagrangian #10
12 Mon, 9/24/2012Chap. 3 & 6 Lagrangian and Hamiltonian #11
13 Wed, 9/26/2012Chap. 6 Lagrangian and Hamiltonian #12
14 Fri, 9/28/2012Chap. 6 Lagrangian and Hamiltonian #13
15 Mon, 10/01/2012Chap. 4 Small oscillations #14
16 Wed, 10/03/2012Chap. 4 Small oscillations #15
17 Fri, 10/05/2012Chap. 4 Small oscillations
18 Mon, 10/08/2012Chap. 7 Wave equation Take Home Exam
19 Wed, 10/10/2012Chap. 7 Wave equation Take Home Exam
20 Fri, 10/12/2012Chap. 7 Wave equation Take Home Exam
21 Mon, 10/15/2012Chap. 7 Wave equation Exam due
22 Wed, 10/17/2012Chap. 7, 5 Moment of inertia
Fri, 10/19/2012 Fall break
23 Mon, 10/22/2012Chap. 5 Rigid body rotation #16
24 Wed, 10/24/2012Chap. 5 Rigid body rotation #17
25 Fri, 10/26/2012Chap. 5 Rigid body rotation #18
26 Mon, 10/29/2012Chap. 8 Waves in elastic membranes #19
27 Wed, 10/31/2012Chap. 9 Introduction to hydrodynamics
28 Fri, 11/01/2012Chap. 9 Introduction to hydrodynamics
29 Mon, 11/05/2012Chap. 9 Introduction to hydrodynamics #20
30 Wed, 11/07/2012Chap. 9 Sound waves
31 Fri, 11/09/2012Chap. 9 Linear sound waves #21
32 Mon, 11/12/2012Chap. 9 Green's function for linear sound
33 Wed, 11/14/2012Chap. 9 Non-linear sound
34 Fri, 11/16/2012Chap. 9 Non-linear sound Take Home Exam
35 Mon, 11/19/2012Chap. 10 Surface waves Take Home Exam
Wed, 11/21/2012 Thanksgiving Holiday
Fri, 11/23/2012 Thanksgiving Holiday
36 Mon, 11/26/2012Chap. 10 Surface waves Exam due
37 Wed, 11/28/2012Chap. 10 Surface waves
38 Fri, 11/30/2012Chap. 10 Surface waves
39 Mon, 12/03/2012 Student presentations I
40 Wed, 12/05/2012 Student presentations II
No Title
PHY 711 - Assignment #1
08/29/2012
PDF file
  1. In evaluating the differential cross section for Rutherford scattering, it is necessary to evaluate the following relationship involving the scattering angle θ, the impact parameter b, and a length parameter κ which involves the ratio of the interaction strength to the system energy:
    π
    2
    		 − θ
    2
    		 = ⌠
    ⌡     		∞

    κ+√{κ2+b2} 
    		 b
    r
    		 1

    √
    r2−2 κr −b2
    		 dr.
    Use Maple or other algebraic manipulation software to evaluate the integral to show that
    b= κ
    tan(θ/2)
    		 .


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On 28 Aug 2012, 17:56.
No Title
PHY 711 - Assignment #2
8/31/2012
  1. In class, we showed that the relationship between the impact parameter b and the scattering angle χ for elastic scattering between two hard spheres has the form:
    b = D cos⎛
    ⎝     		χ
    2
    		⎞
    ⎠     		.
    Using the above diagram which shows the geometry of two hard spheres at the moment of impact, derive this formula.


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On 28 Aug 2012, 18:33.

PHY 711 -- Assignment #3

Sept. 3, 2012

Continue reading Chapter 1 in Fetter & Walecka.

PHY 711 -- Assignment #4

Sept. 5, 2012

Finish reading Chapter 1 and start reading Chapter 2 in Fetter & Walecka.

PHY 711 -- Assignment #5

Sept. 7, 2012

Finish reading Chapter 2 in Fetter & Walecka.

  • Complete the analysis of the Foucault pendulum, using either the method used in the lecture notes or the method used in the text. Estimate the pendulum period for Winston-Salem.

PHY 711 -- Assignment #6

Sept. 10, 2012

Start reading Chapter 3 in Fetter & Walecka.

  • Work problem 3.10 at the end of Chapter 3 of Fetter & Walecka.

PHY 711 -- Assignment #7

Sept. 14, 2012

Continue reading Chapter 3 in Fetter & Walecka.

  • Work problem 3.5 at the end of Chapter 3 of Fetter & Walecka.
No Title
PHY 711 - Assignment #8
9/17/2012
PDF version
  1. The figure above shows a box of mass m sliding on the frictionless surface of an inclined plane (angle θ). The inclinded plane itself has a mass M and is supported on a horizontal frictionless surface. Write down the Lagrangian for this system in terms of the generalized coordinates X and s and solve for the equations of motion, assuming that the system is initially at rest.


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On 16 Sep 2012, 16:08.

PHY 711 -- Assignment #9

Sept. 19, 2012

Continue reading Chapters 3 and 6 in Fetter & Walecka.

  • Work problem 6.5 at the end of Chapter 6 of Fetter & Walecka.

PHY 711 -- Assignment #10

Sept. 21, 2012

Continue reading Chapters 3 and 6 in Fetter & Walecka.

  • Work problem 3.13 at the end of Chapter 3 of Fetter & Walecka. Note: For part d, it is not necessary to solve the full equation. Setting up the equations and showing that they are consistent with the known solution is sufficient.

PHY 711 -- Assignment #11

Sept. 24, 2012

Continue reading Chapters 3 and 6 in Fetter & Walecka.

  • Consider the motion of the particle in the magnetic field given in problem 6.5 part c at the end of Chapter 6 in Fetter and Walekca. Write down the form of the Lagrangian and then determine the Hamiltonian. Determine the canonical equations of motion for the Hamiltonian and show that they lead to the same result you obtained previously.

PHY 711 -- Assignment #12

Sept. 26, 2012

Continue reading Chapter 6 in Fetter & Walecka.

Read parts of the paper by Hans C. Andersen "Molecular dynamics simulations at constant pressure and/or temperature" in which he constructs a Lagrangian function to represent a system of particles held at constant pressure α.

  1. Starting with the Lagrangian function (3.2), derive the Hamiltonian function (3.6).
  2. Derive the equations of motion (3.7).

PHY 711 -- Assignment #13

Sept. 28, 2012

Finish reading Chapter 6 in Fetter & Walecka.

  1. Verify the Hamilton-Jacobi solution to the harmonic oscillator problem we covered in class.
  2. Simplify the expression for the action S(q,t) to show that it is consistent with the action calculated directly from the Lagrangian.

PHY 711 -- Assignment #14

Oct. 01, 2012

Start reading Chapter 4 in Fetter & Walecka.

  1. Work problem 4.2 at the end of Chapter 4 in Fetter & Walecka.

PHY 711 -- Assignment #15

Oct. 03, 2012

Continue reading Chapter 4 in Fetter & Walecka.

  1. Work problem 4.14 at the end of Chapter 4 in Fetter & Walecka.
No Title
Oct 22, 2012
PHY 711 - Problem Set # 16
PDF File
Continue reading Chapter 5 in Fetter and Walecka.



The above figure shows an object with four particles held together with massless bonds at the coordinates shown. The masses of the particles are m1=m2 ≡ 2m and m3=m4 ≡ m.
  1. Evaluate the moment of inertia tensor for this object in the given coordinate system.
  2. Find the principle moments of inertia and the corresponding principle axes. Sketch the location of the axes.


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On 22 Oct 2012, 12:32.
No Title
Oct 24, 2012
PHY 711 - Problem Set # 17
PDF file
Finish reading Chapter 5 in Fetter and Walecka.
In most Classsical Mechanics texts (besides Fetter and Walecka), the Euler angles are defined with a different convention as shown below. (This figure was slightly modified from one available on the website http://en.wikipedia.org/wiki/Euler_angles.)
In this case, the first rotation is about the original ∧z axis by ϕ corresponding to the rotation matrix
ℜϕ = ⎛
⎜
⎜
⎜
⎝
cosϕ
sinϕ
0
−sinϕ
cosϕ
0
0
0
1
⎞
⎟
⎟
⎟
⎠ 		.
(1)
The second rotation is about the new ∧x axis by θ corresponding to the rotation matrix
ℜθ = ⎛
⎜
⎜
⎜
⎝
1
0
0
0
cosθ
sinθ
0
−sinθ
cosθ
 ⎞
⎟
⎟
⎟
⎠ 		.
(2)
In this case, the last rotation is about the new ∧z axis by ψ corresponding to the rotation matrix
ℜψ = ⎛
⎜
⎜
⎜
⎝
cosψ
sinψ
0
−sinψ
cosψ
0
0
0
1
⎞
⎟
⎟
⎟
⎠ 		.
(3)
For this convention, write a general expression for the angular velocity vector ω in terms of the time rate of change of these Euler angles - · ϕ, · θ, and · ψ corresponding to the 29.7 of your text.


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On 24 Oct 2012, 12:50.

PHY 711 -- Assignment #18

Oct. 26, 2012

Finish reading Chapter 5 in Fetter & Walecka.

  1. Work either problem 5.9 or problem 5.10 at the end of Chapter 5 in Fetter & Walecka.

PHY 711 -- Assignment #19

Oct. 29, 2012

Start reading Chapter 8 in Fetter & Walecka.

  1. Work problem 8.5 at the end of Chapter 8 in Fetter & Walecka.

PHY 711 -- Assignment #20

Nov. 05, 2012

Continue reading Chapter 9 in Fetter & Walecka.

  1. Determine the form of the velocity potential for an incompressible fluid representing uniform velocity in the z direction at large distances from a spherical obstruction of radius a. Find the form of the velocity potential and the velocity field for all r > a. Assume that the velocity in the radial direction is 0 for r = a and assume that the velocity is uniform in the azimuthal direction.

PHY 711 -- Assignment #21

Nov. 09, 2012

Continue reading Chapter 9 in Fetter & Walecka.

  1. Work problem 9.3 at the end of Chapter 9 in Fetter & Walecka.
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Last modfied: Wednesday, 28-Nov-2012 14:19:30 EST