PHYSICS 428: QUANTUM MECHANICS III

PHYSICS 428: QUANTUM MECHANICS III
Fall 2023

Instructor: Prof. Michael S. Vogeley
Department of Physics
Office: Disque 811
Email: vogeley@drexel.edu
Office hours: TBA

We are living in a quantum world. Get used to it.

Announcements
Course Meetings
Syllabus
Course Description and Philosophy
Course Outline
Course Learning Outcomes
Textbook and Reading Assignments
Grading
Exams
Course Schedule
Course rules of conduct

ANNOUNCEMENTS:

Welcome back to Drexel and welcome to the home page of QM III. This web page is also the syllabus for the course. See the Blackboard Learn site for this course for details about assignments and exams. Course materials are provided only to registered students at Drexel University.

Course Meetings

We will meet for lectures and discussion on Tuesdays and Thursdays 1:00-2:50pm in Curtis 353A. Our class meetings will include lectures on the course material and problem solving. You should do the reading assignments ahead of time so that you are prepared to ask and answer questions.

Syllabus

This web page is the syllabus. Please print this out and save it and/or bookmark this website for the future. If you're reading a printed copy, and don't remember the URL, you can find the web page at http://www.physics.drexel.edu/~vogeley/Phys428. You should check the Blackboard Learn site frequently for updates about course activities and assignments.

Course Description and Philosophy

Quantum Mechanics (QM hereafter) is one of the foremost intellectual achievements of the 20th century and forms much of the foundation of modern Physics. Many of the giants of Physics (Einstein, Bohr, Pauli, Dirac, Feynmann, et al.) were responsible for its development. Study hard and you will be rewarded by sharing in their insight.

In the first two quarters of our three part sequence on QM, you studied the basic equations, discussed the similarities and differences between the classical and QM descriptions, and solved some simple, typically one-dimensional problems. In the second quarter you worked on QM in three dimensions, including description of the Hydrogen atom, from which you could first see how the QM formulation yields accurate predictions of the observed phenomena, and studied multi-particle systems.

Now you're ready to delve more deeply into QM. Read through the practice problems to tune up your brains after the Summer (and the coop cycle). Then we'll quickly step up to more interesting work. Most problems more complicated than those you solved in QM I and II require use of one approximation scheme or another. Clearly, learning to do Physics is more than just memorizing equations; you need to learn methods for applying them: perturbation theory and the variational principle, for example. We'll examine the interaction of radiation with matter to see how absorption and emission of photons arises from perturbation theory. Then we will study scattering theory which describes how particles interact with each other, as in collisions in a particle accelerator. We will also consider some deep questions and experiments that strike at the core of our understanding of quantum mechanics, including the EPR paradox and Bell's Theorem.

Course Outline


Not necessarily in chronological order:
  1. Review of Principles and Simple Problems
  2. Time-Independent Perturbation Theory (Ch. 7)
    • Nondegenerate Perturbation Theory
    • Degenerate Perturbation Theory
    • The Fine Structure of Hydrogen
    • The Zeeman Effect
    • Hyperfine Splitting
  3. Time-Dependent Perturbation Theory (Ch. 11)
    • Two-level systems
    • Emission and absorption of radiation (Photons!)
    • Spontaneous emission
  4. Variational Principle (Ch. 8)
    • Theory
    • Ground state of Helium
    • Hydrogen molecule ion
  5. Scattering Theory (Ch. 10)
    • Partial wave analysis
    • Phase shifts
    • Born approximation
  6. Deep Questions in Quantum Mechanics (Ch. 12)
    • EPR paradox
    • Bell's theorem
    • No-clone theorem
    • Schroedinger's cat
    • Quantum zeno paradox

Course Learning Outcomes

  1. Apply time-independent perturbation theory to find the fine structure and hyperfine structure of Hydrogen.
  2. Use time-dependent perturbation theory to understand two-level systems, in particular emission and absorption rates of photons.
  3. Apply the variational principle to solve for the ground state of Helium and other simple systems.
  4. Use the methods of partial wave analysis, phase shifts, and the Born approximation to predict results of scattering of particles from simple potentials.
  5. Explain the EPR paradox, Bell's theorem, and the importance of entangled states.

Textbook and Reading Assignments

Required Reading: Introduction to Quantum Mechanics, 3rd edition by David J. Griffiths and Darrel F. Schroeter, 2018, (Cambridge University Press) ISBN-13 978-1316995433, ISBN-10 1107189632. This is the same text that was used for Quantum Mechanics I and II, so most of you should already own it. Other books that I recommend include A Modern Approach to Quantum Mechanics by John S. Townsend, Principles of Quantum Mechanics by R. Shankar, and Quantum Physics by Stephen Gasiorowicz.

See the Course Schedule for the assigned readings, which you should do before class, so that you are prepared to ask and answer questions.

I will also hand out photocopies of selected passages from other QM texts, as necessary to supplement Griffiths.

Grading

Grades will be based on the following weighting of different components of the course:
Problem Sets: 30%
Class Participation (in-class problems): 5%
Midterm Exam: 25%
Final Exam: 40%

Final grades will be assigned following the usual correspondence between percentage scores and letters: 90-100 is A- to A+, 80-89 is B- to B+, etc. However, there may be a positive curve, which means that your letter grade could be higher than in the normal grading scheme (e.g., a 90 is at least an A-).

Problem Sets


There will be seven problem sets. You will have a week to a week and a half to complete each. No late homework will be accepted. Please neatly and accurately write up your solutions to these problems; the notation of QM is quite compact in places and small differences in the equations can have large differences in meaning. I will hand out solutions to the problems on or shortly after their due dates, to give you feedback as quickly as possible.

You may discuss the homework with your classmates, but you and you alone are responsible for the work that you turn in. Please write up your own solutions to the problems. Breaches of this policy will result in homework scores being divided by the number of ``participants.'' Second offenses may result in failure (of the class).

Use of solutions to these problems from previous years constitutes plagiarism. You must attribute (by giving the correct reference) any significant help that you receive from outside sources.

Exams


Any topic covered in lecture, the assigned readings, or homeworks is fair game. I will distribute a non-exhaustive list of "questions to ponder" in advance of each exam to help guide your studying.

The midterm exam will be in class during week 6 and will cover material during the first five weeks or so.

The final exam will be held during exam week (date and location TBA). It will be comprehensive and half closed and half open book. You may bring a calculator to perform numerical calculations only.

Course Schedule

Please note the following schedule of readings and assignments. This schedule may be revised, so you should recheck the week by week course pages in Blackboard Learn. Notation of "HW#" indicates that a homework is due by that Friday. Exact due dates for the homework will be announced in class and on Blackboard Learn. You should do the indicated reading before class.

Week Class Dates Reading Homework Exams
1 September 26, 28 practice problems, Griffiths ch. 7
2 October 3, 5 Griffiths ch. 7 HW1
3 October 10, 12 Griffiths ch. 11 HW2
4 October 17, 19 Griffiths ch. 11 HW3
5 October 24, 26 Griffiths ch. 10 HW4
6 October 31, November 2 Griffiths ch. 10 Midterm Exam in class 11/2
7 November 7, 9 Griffiths ch. 10 HW5
8 November 14, 16 Griffiths ch. 10, 8
9 November 21, (No class 11/23 for Thanksgiving break) Griffiths ch. 8, 12
10 November 28, 30 Griffiths ch. 12 and handouts HW6
11 December 5, 7 Griffiths ch. 12 and handouts HW7
12 No Class Final Exam TBA

Course Rules of Conduct and Academic Policy

Following is an incomplete list of policies. It is your responsibility to be be familiar with and follow all Drexel policies. As the saying goes, "ignorance of the law is no excuse." Also see "More Drexel Policies" on the Blackboard Learn site for this course. Most of this is common sense, but some folks need a gentle reminder.

Electronic distractions: Silence your cell phone. Turn off notifications on your phone and computer so that they don't pop up and distract you.

Plagiarism: Use your own very large brain (you're a physicist!) and don't even think about cheating. The usual University rules apply. By stepping into the classroom, you agree to abide by Drexel's policy on Academic Integrity (www.drexel.edu/provost/policies/academic-integrity/)

Students with disabilities requesting accomodation and services at Drexel University need to present a current accomodation letter (AVL) to faculty before accomodations can be made. This cannot be done retroactively. AVL's are issued by the Office of Disability Services (ODS). For additional information, contact ODS at www.drexel.edu/ods 3201 Arch St., Suite 210, 215-895-1401 (V), or 215-895-2299 (TTY).

Course Add/Drop Policy (www.drexel.edu/provost/policies/course-add-drop)

Course Withdrawal Policy (www.drexel.edu/provost/policies/course-withdrawal)

Drexel Student Code of Conduct (www.drexel.edu/studentlife/community_standards/code-of-conduct/)

Course Syllabus Change policy: Details of this syllabus are subject to change at any time. The Blackboard Learn pages are the official description of the course requirements. Please pay attention to announcements during class and email from the instructor. Significant changes will be announced in writing by email sent to all registered students.

Last update: August 30, 2023