PHY 344 Quantum Mechanics II

MWF 9-9:50 AM OPL 107 http://www.wfu.edu/~natalie/s03phy344/

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

Homework Assignments

Information about Computational Project

PHY 344 -- Assignment #1

January 15, 2003

Read Appendix J of Eisberg and Resnik

  1. Work Problem J.2. The problem suggests that you compare your perturbation theory result with the exact answer obtained in problem H.3. If you have not already worked this problem, you may find the Maple results or Maple file to be helpful.

PHY 344 -- Assignment #2

January 17, 2003

Complete reading of Appendix J of Eisberg and Resnik

  1. Work Problem J.4.

PHY 344 -- Assignment #3

January 27, 2003

Complete reading of the lecture notes on perturbation theory on Appendix K of Eisberg and Resnik

  1. Work through the example given in the lecture notes on using the variational method to estimate the ground state of H.
    1. Verify (or otherwise) the results in the note using a Gaussian shape trial function.
    2. Use the same variational method with an exponential trial function. That is, choose f(r)=e-b r, where now b is a variational parameter. Find the optimal choice of b and find the minimum energy of the H ground state using that choice.
  2. Work problem #1 in Appendix K of your text.

PHY 344 -- Assignment #4

January 29, 2003

Start reading Chapter 8 of Eisberg and Resnik

  1. Work Problem 8.6.

PHY 344 -- Assignment #5

January 31, 2003

Continue reading Chapter 8 of Eisberg and Resnik

  1. Work Problem 8.7.

PHY 344 -- Assignment #6

February 3, 2003

Continue reading Chapter 8 of Eisberg and Resnik

  1. Work Problem 8.10.

PHY 344 -- Assignment #7

February 5, 2003

Continue reading Chapter 8 of Eisberg and Resnik

  1. Work Problem 8.18.
Feb 12, 2003

PHY 344 -- Problem Set PHY 344 - Problem Set #8



  1. Consider the Hamiltonian of a He-like atom with charge Z:
    - (h/2p)2
    2m
    		 Ñ21 - (h/2p)2
    2m
    		 Ñ22 - Ze2
    r1
    		 - Ze2
    r2
    		 + e2
    |r1 - r2|
    		(1)

    Assuming the ground state wave function has singlet spin and the spatial form:

    Y(r1,r2) =   æ
     ú
    Ö
    a3
    pa03
     
    		 e-a(r1+r2)/a0.
    		(2)
    Find the optimal value of a and the corresponding estimate of the ground state energy. For this purpose, you may wish to use the integral
    ó
    õ     		d3r1 d3r2 |Y(r1,r2)|2 e2
    |r1 - r2|
    		 = 5 e2 a
    8 a0
    		 .
    		(3)

File translated from TEX by TTH, version 2.20.
On 13 Feb 2002, 09:18.

PHY 344 -- Assignment #9

February 19, 2003

Continue reading Chapter 9 of Eisberg and Resnik

  1. Work Problem 9.19.

PHY 344 -- Assignment #10

February 21, 2003

Finish reading Chapter 9 of Eisberg and Resnik

  • Consider a neutral Be atom.
    1. Write out the Slater determinant for the ground state electronic wavefunction.
    2. Write out an expression for the exchange energy for this state in terms of the appropriate one-electron wave functions.

    PHY 344 -- Assignment #11

    March 17, 2003

    Finish reading Chapter 10 of Eisberg and Resnik

    1. Work Problem 10.6 in Eisberg and Resnik
    2. Work Problem 10.9 in Eisberg and Resnik

    PHY 344 -- Assignment #12

    March 19, 2003

    Finish reading Chapter 11 of Eisberg and Resnik

    1. Work Problem 11.16 in Eisberg and Resnik
    2. Work Problem 11.17 in Eisberg and Resnik

    PHY 344 -- Assignment #13

    March 21, 2003

    Finish reading Chapter 11 of Eisberg and Resnik

    1. Work Problem 11.21 in Eisberg and Resnik
    2. Work Problem 11.27 in Eisberg and Resnik

    PHY 344 -- Assignment #14

    March 28, 2003

    Start reading Chapter 12 of Eisberg and Resnik

    1. Work Problem 12.3 in Eisberg and Resnik
    2. Work Problem 12.4 in Eisberg and Resnik

    PHY 344 -- Assignment #15

    March 31, 2003

    Continue reading Chapter 12 of Eisberg and Resnik

    1. Work Problem 12.20 in Eisberg and Resnik
    2. Work Problem 12.22 in Eisberg and Resnik

    PHY 344 -- Assignment #15

    April 4, 2003

    Start reading Chapter 13 of Eisberg and Resnik

    1. Work Problem 13.2 in Eisberg and Resnik
    2. Work Problem 13.7 in Eisberg and Resnik

    PHY 344 -- Assignment #17

    April 7, 2003

    Continue reading Chapter 13 of Eisberg and Resnik.

    1. Work out the details of the Kronig-Penny model presented in the handout from Leighton's text. For the example given, construct a plot of E/V versus k for -p/a < k < p/a.

    PHY 344 -- Assignment #18

    April 9, 2003

    Finish reading Chapter 13 of Eisberg and Resnik.

    1. Work Problem 13.11 of Eisberg and Resnik.
    2. Work Problem 13.12 of Eisberg and Resnik.

    PHY 344 -- Assignment #19

    April 14, 2003

    Reading Chapter 14 of Eisberg and Resnik.

    1. Work Problem 14.2 of Eisberg and Resnik.

    PHY 344 -- Assignment #20

    April 21, 2003

    Read Chapter 15 of Eisberg and Resnik.

    1. Work Problem 15.15 of Eisberg and Resnik.

    PHY 344 -- Assignment #21

    April 23, 2003

    Read Chapter 15 of Eisberg and Resnik.

    1. Work Problem 15.23 of Eisberg and Resnik.

    PHY 344 -- Assignment #22

    April 25, 2003

    Read Chapter 16 of Eisberg and Resnik.

    1. Work Problem 16.6 of Eisberg and Resnik.
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