PHY 741 Quantum Mechanics

MWF 12 PM - 12:50 PM OPL 103 http://www.wfu.edu/~natalie/f17phy741/

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

Course schedule

(Preliminary schedule -- subject to frequent adjustment.)
DateF&W ReadingTopic AssignmentDue
1 Mon, 8/28/2017Chap. 1 Review of basic principles #19/6/2017
2 Wed, 8/30/2017Chap. 1 Linear vector spaces #2 9/6/2017
3 Fri, 9/01/2017Chap. 1 Linear vector spaces #39/6/2017
4 Mon, 9/04/2017Chap. 4 Principles of Quantum Mechanics #49/8/2017
5 Wed, 9/06/2017Chap. 5 Examples in 1 dimension
6 Fri, 9/08/2017Chap. 5 Schrödinger equation in one-dimension #59/13/2017
7 Mon, 9/11/2017Chap. 5 Schrödinger equation in one-dimension
8 Wed, 9/13/2017Chap. 7 Schrödinger equation in one-dimension #69/15/2017
9 Fri, 9/15/2017Chap. 7 Schrödinger equation in one-dimension #79/20/2017
10 Mon, 9/18/2017Chap. 5 and 7 Schrödinger equation in one-dimension
11 Wed, 9/20/2017Chap. 9 Commutator formalism #89/22/2017
12 Fri, 9/22/2017Chap. 10 Quantum mechanics of multiparticle systems #99/25/2017
13 Mon, 9/25/2017Chap. 10-12 Multiparticle systems and angular momentum
14 Wed, 9/27/2017Chap. 12 Eigenstates of angular momentum
15 Fri, 9/29/2017Chap. 1,4,5,7,9,10,12 Review
Mon, 10/02/2017 Take-home exam -- No class
Wed, 10/04/2017 Take-home exam -- No class
16 Fri, 10/06/2017Chap. 12-13 Spherically symmetric systems
17 Mon, 10/09/2017Chap. 13 Quantum mechanics of a hydrogen atom #1010/16/2017
18 Wed, 10/11/2017Chap. 13 Quantum mechanics of multi-electron atoms
Fri, 10/13/2017 Fall break -- No class
19 Mon, 10/16/2017 Discuss exam questions and topics for presentations Topic10/18/2017
20 Wed, 10/18/2017Chap. 14 Intrinsic spin #1110/20/2017
21 Fri, 10/20/2017Chap. 15 Addition of Angular Momentum #12 10/23/2017
22 Mon, 10/23/2017Chap. 15 Multi-electron atoms #13 10/25/2017
23 Wed, 10/25/2017Chap. 15 Multi-electron atoms #14 10/30/2017
24 Fri, 10/27/2017 Effects of nuclear motion
25 Mon, 10/30/2017Chap. 17 Time-independent perturbation theory #15 11/3/2017
26 Wed, 11/01/2017Chap. 17 Time-independent perturbation theory
27 Fri, 11/03/2017 Effects of a static magnetic field
28 Mon, 11/06/2017Chap. 18 Time-dependent perturbation theory #16 11/10/2017
29 Wed, 11/08/2017Chap. 18 Time-dependent perturbation theory
30 Fri, 11/10/2017Chap. 19 Scattering theory #17 11/15/2017
Mon, 11/13/2017 Class cancelled
31 Wed, 11/15/2017Chap. 19 Scattering theory
32 Fri, 11/17/2017Chap. 20 Dirac Equation
33 Mon, 11/20/2017Chap. 20 Dirac Equation
Wed, 11/22/2017 Thanksgiving Holiday -- No class
Fri, 11/24/2017 Thanksgiving Holiday -- No class
34 Mon, 11/27/2017Chap. 20 Dirac Equation
35 Wed, 11/29/2017Chap. 20 Dirac Equation
36 Fri, 12/01/2017Chap. 1-20 Review
Mon, 12/04/2017 Presentations I
Wed, 12/06/2017 Presentations II
Fri, 12/08/2017 Presentations III
No Title
PHY 741 - Assignment #1
PDF Version
08/28/2017
Read Chapter 1 of Shankar.
  1. Consider a 3-dimensional vector space with three non-orthogonal vectors | v1 〉, | v2 〉, and | v3 〉, where
    | v1 〉=
    ^
    x
     
    		 +
    ^
    y
     
    		 +
    ^
    z
     

    | v2 〉=
    ^
    x
     
    		 +
    ^
    y
     
    		 −
    ^
    z
     

    | v3 〉=
    ^
    x
     
    		 −
    ^
    y
     
    		 +
    ^
    z
     
    		 .
    Use the Gram-Schmidt procedure to form 3 orthonormal vectors | w1 〉, | w2 〉, and | w3 〉. Determine expressions for | w1 〉, | w2 〉, and | w3 〉 in terms of ∧x, ∧y, and ∧z.


File translated from TEX by TTH, version 4.01.
On 27 Aug 2017, 21:14.

PHY 741 -- Assignment #2

Aug. 30, 2017

Read Chapter 1 in Shankar .

  • Work problem 1.8.5 on page 42 of your textbook.
    No Title
    PHY 741 - Assignment #3
    PDF Version
    09/01/2017
    Continue reading Chapter 1 of Shankar.
    1. Evaluate the following integral over a Dirac delta function:
      ⌠
      ⌡       		∞

      −∞ 
      		 δ(x2−3x+2) dx.


    File translated from TEX by TTH, version 4.01.
    On 31 Aug 2017, 22:31.

    PHY 741 -- Assignment #4

    Sep. 4, 2017

    Read Chapter 4 after skimming Chapters 2 and 3 in Shankar .

  • Work problem 4.2.1 on page 129 of your textbook.

    PHY 741 -- Assignment #5

    Sep. 8, 2017

    Continue reading Chapter 5 in Shankar .

  • Work problem 5.2.6 on page 164 of your textbook, numerically finding the discrete energy eigenvalues when V0=4ℏ2/(2ma2). (It is not necessary to explicitly answer questions 1-3.)

    PHY 741 -- Assignment #6

    Sep. 13, 2017

    Continue reading Chapter 5 in Shankar .

  • Verify (or otherwise) the equations presented in Lecture 7 concerning the scattering of a matter wave of energy E corresponding to a particle of mass m moving along the x-axis in a potential that is 0 for x<0 and V0 for x>0.

    PHY 741 -- Assignment #7

    Sep. 15, 2017

    Continue reading Chapter 7 in Shankar .

  • Work problem #7.4.4 on page 212 of Shankar.

    PHY 741 -- Assignment #8

    Sep. 20, 2017

    Read Chapter 9 in Shankar .

    • Consider the operators X and P representing displacement and momentum along the x-axis. Evaluate the following commutators: [X,P2] and [X2,P].

    PHY 741 -- Assignment #9

    Sep. 22, 2017

    Read Chapter 10 in Shankar .

    • Work problem 10.3.3 on page 277 of Shankar .

    PHY 741 -- Assignment #10

    Oct. 09, 2017

    Read Chapter 13 in Shankar .

    • Using the variational method, estimate the ground state energy of a hydrogen like atom with Z protons using the variation approach and the trial wavefunction shape of ψ = e-α r2, optimizing with respect to the α parameter.

    PHY 741 -- Assignment #11

    Oct. 18, 2017

    Read Chapter 14 in Shankar .

    • Work problem 14.3.5 in Shankar.

    PHY 741 -- Assignment #12

    Oct. 20, 2017

    Read Chapter 15 in Shankar .

    • Express all of the eigenstates of total j and m composed of the direct product states of l=1 m and s=1/2 ms.

    PHY 741 -- Assignment #13

    Oct. 23, 2017

    Read Chapter 15 in Shankar .

    • Account for number of two particle states corresponding to the configuration 3d2 as discussed in class. Show that the same number of states are present in the atomic term representation 2S+1LJ.
    No Title
    PHY 741 - Assignment #14
    PDF VERSION
    10/25/2017
    Finish reading Chapter 15 of Shankar.
    1. Evaluate the radial Coulomb integrals ℜλ(2p,2p;2p,2p) for λ = 0,2 when the radial wavefunction has the form in terms of constants Z and a0.
      R2p(r)=⎛
      ⎝       		Z
      2a0
      		⎞
      ⎠       		3/2

       
      		 Zr
      √3 a0
      		 e−Zr/(2a0).


    File translated from TEX by TTH, version 4.01.
    On 25 Oct 2017, 00:25.

    PHY 741 -- Assignment #15

    Oct. 30, 2017

    Read Chapter 17 in Shankar .

    • Work problem 17.2.5 on page 457 of Shankar.

    PHY 741 -- Assignment #16

    Nov. 6, 2017

    Read Chapter 18 in Shankar .

    • Work problem 18.2.4 on page 478 of Shankar. Instead of the given final state, compute the probability for the system to be in the state |n=2,l=0,m=0>.

    PHY 741 -- Assignment #17

    Nov. 10,, 2017

    Read Chapter 19 in Shankar .

    • Work problem 19.5.2 on page 553 of Shankar.
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    Last modfied: Friday, 17-Nov-2017 01:20:57 EST