Quantum Mechanics

PHYS 421 Spring 2012

Announcements:

• Complete Online Evaluations for your TA and Professor: instructions are posted here. I will add extra 2 pts to your final score (max =100) for thoughfully evaluating this awesome class.
• Bonus problem meeting time: dead day @ 9:30 AM in physics computer lab.
• BONUS Problem posted.
• Test # 2 is rescheduled: new date Apr. 10 (Tue).
• Mathematica demo of Gaussian wavepacket dynamics (courtesy of Dr. J. Weinstein)
• Here (courtesy of Dr. J.Weinstein) is the Mathematica file that I used for in-class demonstration. To explore this demo you would need to install Mathematica player. Nope, you do not need to know the very powerful Mathematica language to play with the demos.
• Some of you have asked about late homework policy. So let's make it explicit: there is a 10 point penalty for each late day. No late HW will be accepted after one week.
• Revised office hours: every Thursday 2-3pm.
• Test #1 is scheduled for Th., Feb. 23. This is a closed-book test. You may use you mind/memory-maps (follow this link) for Ch.1 and Ch.2 (Sections 2.1 and 2.2).
• HW solutions are placed on reserve at the De LaMare library.
• Welcome to the wonderful mysteries of quantum mechanics!
  

BONUS Problem due May 1st

If fully completed, this will add 10 bonus ponts to your score.
(a) Using Numerov method + shooting algorithm, NUMERICALLY solve the 1D S.E. for the ground state w.f. and energy of a potential V(x) supporting bound states (see Ch.3 of Koonin & Meredith book on reserve at the library). You could use any programming language.
(b) Demonstrate the accuracy of your solution for the HO potential.
(c) Find numerically the ground state energy of V(x)=A( exp[-2 a x] - 2 exp[-a x] ). Here A and a are adjustable parameters Sqrt[ 2m A] > 1/2 a hbar.
You will need to provide me with a clear description of your code, code printout, output for (b) and (c), and I will schedule a meeting in a computer lab, where you will demonstrate solving (c) for my set of input parameters. DO NOT send me executable files.

Catalog description:  [3 credits]

Wave-particle duality, Schroedinger equation, probability density, particle in a box, harmonic oscillator, operators, eigenvalues, eigenfunctions. Prerequisites: PHYS 182; PHYS 301

Time: 09:30 A.M. - 10:45 A.M.
Days:  Tue & Th
Location: LP 105

Instructor: Dr. Andrei Derevianko   
  E-mail : andrei_AT_unr.edu (replace _AT_ with @)   
  Office: LP 200 
  Phone: x46039 

Office hours: Every Thursday, 2:00PM-3:00PM and by appointment.

Textbook: 
Required: David J. Griffiths, "Introduction to Quantum Mechanics", second edition, Prentice Hall, 2005. Here is the erratum.
Up to date reading of the textbook material is a standing homework assignment.

Important dates:

Your grade:
    5% attendance, 25% homework, 20% test#1, 20% test#2, 30% final exam.

Tests: 
    There will be two written tests and the final written exam.

Homework Assignments:  

Problem sets will be announced in class and/or posted on this web page usually each Tuesday. The HW will be due one week later at the beginning of the class. I will grade a random subset of your work. The homework will make up 25% of the overall score - if you submit it regularly.

The solutions will be placed on reserve at the De LaMare library on a regular basis. Up to date reading of the textbook material is a standing homework assignment. For your convenience, I will provide you with textbook sections to be covered each week.

• HW# 0 (due Tue Jan. 31)
  (1) Understand Chapter 1. To better assimilate this truly foundational material draw a memory/mind map (follow this link) and turn it in.
  (2) Send me an e-mail with a subject line "QM class", so I have your most recent address.
• HW# 1 (due Tue Feb. 7)
  (1) (20 pts) 1.1  [distribution of ages]
  (2) (20 pts) 1.3  [<x>,<x^2> etc, Gaussian distribution ]
  (3) (25 pts) 1.5*  [w.f. normalization]
  (4) (35 pts) 1.7*  [Ehrenfest's theorem]
• HW# 2 (due Tue Feb. 14)
  (1) (25 pts) 1.14  [1D probability current]
  (2) (15 pts) 1.18  [QM regimes for solid and gas phases]
  (3) (30 pts) 2.1*  [Im(E)=0, phi(x) can be chosen real, odd/even V and spectrum]
  (4) (30 pts) 2.2* [E > min V(x)]
• HW# 3 (due Tue Feb. 21)
  (1) (10 pts) By plugging Eq.(2.15) into the time-dependent Schroedinger equation, prove that it is indeed the correct solution.
  (2) (30 pts) 2.4* [<x>,<x2>,<p>, etc & uncertainty relation for inf-deep square well]
  (3) (30 pts) 2.5*[ linear combination of stationary states (well)]
  (4) (30 pts) 2.7*[ Psi(x,t) given Psi(x,t=0); P(E1),<H> (well)]
  
• HW# 4 (due Tue Feb. 28)
  (1) (30 pts) 2.8 [Psi(x,t=0) in half well;  P(En)]
  (2) (40 pts) 2.38* [well; sudden expansion; P(En)]
  (3) (30 pts) 2.39 [revival time in an infinite square well]
• HW#5 (Due Tue Mar 6)
  (0) (30 pts) Draw memory map for Section 2.3
  (1) (35 pts) 2.37 [well; time evolution; <H>]
  (2) (35 pts) Derive Eq.(2.53) and (2.56) [ladder operators & Hamiltonian HO]
• HW#6 (Due Tue Mar 13)
  (1) (10 pts) Evaluate commutators of ladder operators (I need to see details)
  (2) (30 pts) Problem 2.12* [ladder operators and <x>, <x^2>,... for HO]
  (3) (30 pts) Problem 2.13 [superposition of the HO states]
  (4) (30 pts) Problem 2.14 [sudden change w->2w HO]
• HW#7 (Due Tue Mar 27)
  (0) (20 pts) Draw memory map for Sections 2.4 and 2.5
  (1) (20 pts) Derive Eq.(2.72),(2.78) and (2.80). Show details. [Series solution for HO]
  (2) (25 pts) Using Mathematica or any other plotting program (e.g., Excel), plot HO wave functions for n=0,1,2, and 100. I invite you to challenge yourself by making as many qualitative observations about these plots as you can.
  (3) (35 pts) Problem 2.17** (various properties of Hermite polynomials)
• HW#8 (Due Tue Apr 3)
  (1) (20 pts) Problem 2.19 [probability current, free particle]
  (2) (20 pts) Problem 2.21 [ momentum representation for A exp(-a|x|) ]
  (3) (60 pts) Problem 2.22* [ Gaussian wavepacket]
• HW#9 (Due Tue Apr 10; this is the date of test #2 )
  (1) (25 pts) Problem 2.23* [integrals with delta-function]
  (2) (35 pts) Problem 2.26* [Fourier transform of delta-function]
  (3) (40 pts) Problem 2.27* [Double delta-function potential]
• HW#10 (Due Tue Apr 17)
  (1) (100 pts) Problem 2.28** [Transmission coefficient for double delta-function potential]
• HW#11 (Due Tue Apr 24)
  (1) (50 pts) A-2, A-8, A-9 from the Appendix
  (3) (25 pts) Problem 3.3 [Hermicity for <f|Q|g>]
  (4) (25 pts) Problem 3.4 [props of Hermitian ops]
• HW#12 (Due Tue May 1st)
  (0) (20 pts) Draw memory map for Chapter 3
  (1) (20 pts) Problem 3.5 [Hermitian conjugate/adjoint operator]
  (2) (20 pts) Problem 3.6 [d^2/dphi^2 operator]
  (3) (20 pts) Problem 3.7 [degenerate spectrum props]
  (4) (20 pts) Problem 3.8 [reality of eigenvals of Hermitian operators]
• The last HW (Due Tue May 8th)
  (1) (25 pts) Problem 3.11 [HO ground state in momentum space]
  (2) (25 pts) Problem 3.27 [Sequential measurements]
  (3) (25 pts) Problem 3.22 [bras vs kets and mels of an operator]
  (4) (25 pts) Problem 3.23 [Dirac notation and eigsys for a 2-level system]
  
  

Disability Statement: Any student with a disability needing academic adjustments or accommodations is requested to contact the Disability Resource Center (Thompson Building Suite 101) at the University of Nevada, Reno, as soon as possible to arrange for appropriate accommodations.
Audio/Video recording policy: Surreptitious or covert video-taping of class or unauthorized audio recording of class is prohibited by law and by Board of Regents policy. This class may be videotaped or audio recorded only with the written permission of the instructor. In order to accommodate students with disabilities, some students may have been given permission to record class lectures and discussions. Therefore, students should understand that their comments during class may be recorded.  

URL of this document: http://wolfweb.unr.edu/~andrei/Teaching/phys421.htm
Last modified: May 1, 2012