PHYSICS 327: QUANTUM MECHANICS II

PHYSICS 327: QUANTUM MECHANICS II
Winter 2022-2023

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
Grading
Problem Sets
Exams
Course Schedule
Course rules of conduct

ANNOUNCEMENTS:

This web page is merely 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 Mondays and Wednesdays 9:00-10:50 a.m. in Curtis 456. 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/Phys327. 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 second quarter of our three part sequence on QM, 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 (if there's time) perturbation theory.

Course Outline


Here are the topics we'll cover in QM II

  1. Quantum Mechanics in Three Dimensions (Ch. 4)
    • The Schroedinger Equation in Three Dimensions
    • The Hydrogen Atom
    • Angular Momentum
    • Spin
  2. Identical Particles (Ch. 5)
    • Two-Particle Systems
    • Atoms
    • Solids
    • Quantum Statistical Mechanics
  3. Time-Independent Perturbation Theory (Ch. 7)
    • Nondegenerate Perturbation Theory
    • (maybe) Degenerate Perturbation Theory

Course Learning Outcomes

  1. Solve for the eigenstates and energies of a single particle in three dimensions for the case of central potential.
  2. Understand the detailed structure of the wave function for Hydrogen and hydrogen-like atoms.
  3. Compute properties of systems including orbital angular momentum and spin, including magnetic moments.
  4. Solve for the eigenstates and energies of multiple particle systems such as occur in simple atoms and solids.
  5. Find most probable configurations and energies of many-particle, many-level systems using quantum statistical mechanics.
  6. Use knowledge of the eigenstates and energies of simple systems and approximation methods to solve for energies of perturbed systems.

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 III, so buy it if you do not already own a copy from QMI.

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

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:
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


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 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).

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 the Blackboard Learn site for problem set assignments.

Exams


The midterm will be in class on Wednesday, February 15. This exam will be open book (textbook, your notes, my handouts, your problem sets, my solutions).

The final exam wil be during exam week (date and time TBA). Material on the final exam will be roughly 1/3 from the first half of the course, 2/3 from the second half. This exam will be half closed and half open book (textbook, your notes, my handouts, your problem sets, my solutions).

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 Friday at the start of class. Exact due dates for the homework will be announced in class. You should do the indicated reading before class.

Week Class Dates Reading Homework Exams
1 January 9, 11 4.1
2 January 18 (no class on 1/16) 4.2, 4.3 HW1
3 January 23, 25 4.4 HW2
4 January 30, February 1 4.4 HW3
5 February 6, 8 5.1 HW4
6 February 13, 15 5.2 (and extra readings) Midterm in class 2/15
7 February 20, 22 5.3 HW5
8 February 27, March 1 Extra reading (see Learn) HW6
9 March 6, 8 Extra reading (see Learn) HW7
10 March 13, 15 7.1 HW8
11 Exam Week 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. Meetings on Zoom are more relaxed in some respects, but stil require that we all adhere to some basic rules to stay focused.

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. 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: January 2, 2023