PHY 741 Classical Mechanics

MWF 11-11:50 AM OPL 107 http://www.wfu.edu/~natalie/f04phy741/

Instructor: Natalie Holzwarth Phone:758-5510Office:300 OPL e-mail:natalie@wfu.edu

Homework Assignments

PHY 741 -- Assignment #1

August 25, 2004

Read Chapter 1 in Gottfried & Yan.

PDF file with assignment

PHY 741 -- Assignment #2

August 27, 2004

Read Chapter 2.1-2.4 in Gottfried & Yan.

PDF file with assignment

PHY 741 -- Assignment #3

August 30, 2004

Continute reading Chapter 2.1-2.4 in Gottfried & Yan.

PDF file with assignment

PHY 741 -- Assignment #4

Sept. 1, 2004

Continue reading Chapter 2 in Gottfried..

  1. Consider three non-commuting operators A, B, and C. Show that:
    [AB,C] = A[B,C]+[A,C]B
    [A,BC] = [A,B]C+B[A,C]
  2. Evaluate the commutation relations [x,p2].

PHY 741 -- Assignment #5

September 3, 2004

Continute reading Chapter 2.1-2.4 in Gottfried & Yan.

PDF file with assignment

PHY 741 -- Assignment #6

Sept. 6, 2004

Continue reading Chapter 2 in Gottfried..

An electron of charge -e is moving in a potential field V(r). Consider the effects of a constant magnetic field oriented along the z axis having the form: B = B0 z.

  1. Show that this magnetic field can be described by either of the following vector potentials:
    A1 = (-yx + xy) B0/2
    or
    A2 = -yx B0.
  2. Write out the form of the Schrödinger equation for the electron in each of these cases.
  3. Find the factor that relates the solutions Ψ1 and Ψ2.

PHY 741 -- Assignment #7

Sept. 8, 2004

Continue reading Chapter 3 in Gottfried..

Choose two different values for the eigenvalue j and write out the matrices corresponding to the following operators in the |jm> basis.

  1. J-
  2. J+
  3. Jx
  4. Jy
  5. Jz

PHY 741 -- Assignment #8

Sept. 13, 2004

Continue reading Chapter 3 in Gottfried..

Consider a spin 1/2 system in the |jm> representation, that is in terms of eigenstates of J2. Determine the rotation matrix D(R) in two different ways for the rotation δθ = δθ (x+y).

  1. Using Eq. 79 in chapter 3 of your text.
  2. By figuring out the Euler angles α, β, and γ for this rotion and use Eq. 148 in chapter 7 of your text.

PHY 741 -- Assignment #9

Sept. 15, 2004

Continue reading Chapter 3 in Gottfried..

  1. Work problem 6 on page 164 of your text.
  2. Work problem 8 on page 164 or your text.

PHY 741 -- Assignment #10

Sept. 20, 2004

Continue reading Chapter 3 in Gottfried..

Consider Eqs. 129 & 130 on page 131 of your text.

  1. Evaluate both sides of the equations for the case that k and r are parallel and convince yourself that the equation is true for this case.
  2. Evaluate both sides of the equation for small values of kr by expanding both sides of the equation to order (kr)2. Convince yourself that the equation is true for this case.

PHY 741 -- Assignment #11

September 22, 2004

Continute reading Chapter 3 in Gottfried & Yan.

PDF file with assignment

PHY 741 -- Assignment #12

Sept. 27, 2004

Continue reading Chapter 3 in Gottfried..

  1. Work problem 10 on page 164 of your text.

PHY 741 -- Assignment #13

Sept. 29, 2004

Continue reading Chapter 3 in Gottfried..

  1. Consider an infinite potential well with a particle of mass m confined in the space 0 ≤ x ≤ a.
    1. Divide the interval into N segments and using the central difference approximation, set up the numerical eigenvalue problem.
    2. Using Maple solve the eigenvalue problem for the first 3 eigenvalues using two different choices of N.
    3. (Extra credit) Work the same problem using the Numerov technique.

    PHY 741 -- Assignment #14

    Oct. 4, 2004

    Start reading Chapter 4 in Gottfried..

    1. Work Problem 4.1 on page 228 of Gottfried.

    PHY 741 -- Assignment #15

    Oct. 18, 2004

    Start reading Chapter 5 in Gottfried..

    1. Work Problem 5.9 on page 264 of Gottfried.

    PHY 741 -- Assignment #16

    Oct. 20, 2004

    Continue reading Chapter 5 in Gottfried..

    1. Work Problem 5.12 on page 265 of Gottfried.

    PHY 741 -- Assignment #17

    October 25, 2004

    Continue reading Chapter 6 in Gottfried & Yan.

    PDF file with assignment

    PHY 741 -- Assignment #18

    Oct. 27, 2004

    Continue reading Chapter 6 in Gottfried..

    1. Work Problem 6.5 on page 280-281 of Gottfried.

    PHY 741 -- Assignment #19

    Nov. 3, 2004

    Continue reading Chapter 6 in Gottfried..

    Consider the atomic configuration nd2.

    1. Enumerate all of the atomic terms in the form (2S+1)L, checking that all 45 states are accounted for.
    2. Using the programs "gaunt" and "clebsch" in the directory /users/faculty/phy/natalie/www-home/f04phy741/computer_programs, determine the Coulomb interaction integrals for at least one of them.
    3. Go to the NIST web site http://www.nist.gov and the atomic energy level database to qualitatively compare the experimental configurations with your analysis of the terms.

    PHY 741 -- Assignment #20

    Nov. 5, 2004

    Continue reading Chapter 6 in Gottfried..

    This assignment uses the computer program "graphatom" to model many electron atoms within density functional theory. The web page http://www.wfu.edu/~natalie/s04phy345/ contains additional information beyond what was presented in class. This year, the computer program is accessed with the command /users/faculty/phy/natalie/www-home/f04phy741/computer_programs/graphatom/graphatom

    1. After logging into your wfu.edu account, issue the commands
      mkdir (atom name)
      cd (atom name)
      /users/faculty/phy/natalie/www-home/f04phy741/computer_programs/graphatom/graphatom
      (enter atomic data for neutral atom)

      After the program completes, record the total energy.
    2. Run the same sequence for the corresponding positive ion: cd ..
      mkdir (ion name)
      cd (ion name)
      /users/faculty/phy/natalie/www-home/f04phy741/computer_programs/graphatom/graphatom
      (enter atomic data for positive ion)

      After the program completes, record the total energy.
    3. From the previous results, determine the ionization energy of your atom and compare with experimental results listed at http://www.nist.gov.
    4. (Extra credit) Plot the radial wavefunctions and densities for your atom and ion.

    PHY 741 -- Assignment #21

    Nov. 11, 2004

    Continue reading Chapter 8 in Gottfried..

    1. Work Problem 8.3 on page 398 of your text.

    PHY 741 -- Assignment #22

    Nov. 12, 2004

    Continue reading Chapter 8 in Gottfried..

    1. Consider the partial wave representation of the scattering amplitude derived in class (given in Eq. 20 on page 339 of your text). Show that this form is consistent with the optical theorem (Eq. 54 of your text).

    PHY 741 -- Assignment #23

    Nov. 15, 2004

    Continue reading Chapter 8 in Gottfried..

    1. Work problem 8.6 on page 399 of Gottfried

    PHY 741 -- Assignment #24

    Nov. 19, 2004

    Continue reading Chapter 8 in Gottfried..

    1. Work problem 8.10 on page 399 of Gottfried
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