PHYSICS 326: QUANTUM MECHANICS I

PHYSICS 326: QUANTUM MECHANICS I
Fall 2022

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

Animation of an excited state of Hydrogen, by Drexel student Glenn Winship.

Announcements
Course Meetings
Syllabus
Course Description and Philosophy
Course Outline
Course Learning Outcomes
Textbook and Reading Assignments
Extra Notes
Grading
Problem Sets
Problem Set Solutions
Problem Hints
Exams
Course Schedule
Course rules of conduct

ANNOUNCEMENTS:

Welcome to the home page of QM I. 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 Meetings

We will meet for lectures on Tuesdays and Thursdays 11:00 - 12:50 p.m. in (room TBA). Our class meetings will be a mix of lecture and problem solving. You should do the reading assignments ahead of time so that you are prepared to ask and answer questions.

I will post a password-protected link to Zoom on the Drexel Learn site, to be used for remote office hours or for lectures in the event that we cannot meet in person.

Syllabus

This web page is the syllabus. Please print this out and save it and/or bookmark this website for the future (no printed copies will be distributed). 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/Phys326. 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 this first quarter of our three part sequence on QM, you will study the basic equations, discussed the similarities and differences between the classical and QM descriptions, and solve some simple, typically one-dimensional problems. In the second quarter, we'll move on to three dimensional problems, and the QM description of the Hydrogen atom, from which you could first see how the QM formulation yields accurate predictions of the observed phenomena, and begin study of multi-particle systems and perturbation theory. In the final quarter, we'll delve into more advanced topics include time-dependent perturbation theory (interaction of matter and light), the variational principle, scattering theory, the EPR paradox, Bell's Theorem, and a deeper look at the interpretation of QM.

Course Outline


Here are the topics we'll cover in QM I

  1. The Wave Function (Ch. 1)
    • The Schroedinger Equation
    • Statistical Interpretation
    • Probability
    • Normalization
    • Momentum
    • The Uncertainty Principle
  2. The Time-Independent Schroedinger Equation (Ch. 2)
    • Stationary States
    • Infinite Square Well
    • Harmonic Oscillator
    • Free Particle
    • Delta-Function Potential
    • Finite Square Well
  3. Formalism of Quantum Mechanics (Ch. 3)
    • Hilbert Space
    • Observables
    • Eigenfunctions of a Hermitian Operator
    • Generalized Statistical Interpretation
    • Uncertainty Principle
    • Dirac Notation

Course Learning Outcomes

  1. Explain the meaning of Schroedinger's equation and the probabilistic nature of quantum mechanics.
  2. Understand the relationship between classical observable and quantum mechancial operators.
  3. Explain the origin and implications of the uncertainty principle.
  4. Solve for the eigenstates and energies of a single particle in various one-dimensional potentials (time-independent Schroedinger equation).
  5. Understand the formalism of quantum mechanics, including Hilbert Space, eigenfunctions of Hermitian operators, and Dirac notation.

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 text will also be used for Quantum Mechanics II and III, so buy it!

See the course outline above for the chapters that correspond to the material covered in this course.

Extra Notes

This is a brief (5 page) review of important Fourier transform properties and their relation to the free-particle wavefunction:
Fourier notes (PDF)

Grading

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

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 (check for hints down below!)


There will be eight 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 post 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).

You must give the full citation of any outside source that you employ in your solutions. Use of solutions to these problems from previous years or from other outside sources (including web pages that you find by googling for solutions to Griffiths) constitutes plagiarism and may result in failure (of the course).

Problem sets must be submitted using Blackboard Learn by the due date and time as a legible PDF file (leave extra time to make a single easily readable PDF of your work). Do not send by email. See Blackboard Learn site for problem set assignments.

Problem Set Solutions


See Blackboard Learn site for problem set solutions.

Hints on Problems


See Blackboard Learn site for problem hints.

Exams


The midterm will be during week 6.

The final exam will during the week of December 5-9.

Typical format for both exams is half closed and half open book. "Open book" means that you may consult your own notes, your own homework, solutions and handouts that I have provided, and the assigned textbook.

Course Schedule

Please note the following schedule of readings and assignments. This schedule may be revised, so you should recheck this web page. Notation of "HW#" indicates that a homework is due that week, typically in class on Wednesday. See the Blackboard Learn site for exact due dates for the homework. You should do the indicated reading before class.

Week Class Dates Reading Homework Exams
1 September 20, 22 1.1-1.6
2 September 27, September 29 2.1, 2.2 HW1
3 October 4, 6 2.3, 2.4 HW2
4 October 11, 13 2.5 HW3
5 October 18, 20 2.6 HW4
6 October 25, 27 3.1 Midterm exam
7 November 1, 3 3.2, 3.3 HW5
8 November 8, 10 3.4, 3.5 HW6
9 November 15, 17 3.6 HW7
10 November 22 (no class 11/24 - Thanskgiving break)
11 November 29, December 1 Finish through ch. 3, Review Session HW8
12 December 5-9 Exam Week Final Exam

Course Rules of Conduct and Academic Policies

Following is an incomplete list of policies. It is your responsbility 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.

Food: Our class meetings are at lunchtime and everyone has to eat sooner or later. So eat if you must. Thankfully, we don't yet have Smellivision.

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. Please pay attention to announcements during class and email from the instructor. All changes will be announced in writing by email sent to all registered students.

Last update: September 1, 2022