# PHY 409 Quantum Mechanics: Spring 2024

MWF 1:45pm - 2:50pm in Bracy 237

## Instructor Information

Dr. Julie Butler

Email: butlerju@mountunion.edu

Office: Bracy 107

Office Hours: Monday 11:00am - 12:30pm, Tuesday 2:30pm - 4:00pm, Friday 12:30pm - 1:30pm, or by appointment

Cell Phone: 864-993-7133

Course Description and Learning Objectives

Historical introduction, uncertainty principle, barrier penetration, Hilbert space, Schrodinger formulation, Heisenberg formulation, SU groups, operator concepts, Poisson, Lagrange, and commutator brackets, Dirac four-vectors, introduction to field quantization, and perturbation theory are among the topics presented.

Below are the broad learning objectives for the course. More specific learning objectives will be provided on a chapter-by-chapter basis. This course will cover at least the first seven chapters of Quantum Mechanics (3rd ed.) by David Griffiths and Darrell Schroeter. Additional content may be added due to student interest.

Be able to find expectation values for a variety of operators.

Derive the wavefunction for a particle in an infinite well, a finite well, a delta potential, and a free particle.

Formulate a description of a particle in a harmonic oscillator potential using ladder operators.

Format a problem using the wave mechanics notaion of quantum mechanics as well as Dirac's bra-ket notation.

Use the Schrodinger equation in three dimensions with spherical coordinates to describe the hydrogen atom.

Use angular momentum and spin to describe quantum mechanical systems.

Formlate quantum mechanical descriptions for a two-particle system, atoms, and solids.

Be able to explain and use translation, rotation, and parity as well as their relevant symmetries and conservation laws.

Use pertubation theory to approximate the energy of a quantum mechanical system.

## Course Policies

Student Expectations:

All students are expected to come to class ready to learn and help contribute to an environment that allows other students to learn. This means arriving on time and participating in lectures, not creating distractions for other students, and being courteous to students and the professor.

It is expected that you completed all graded assignments and submit them on D2L by the posted deadline unless you are using an extension as detailed in the late policy.

Attendance Policy: Attendance at all lab sessions is required, but attendance at lectures is not required and will not be taken. If you choose not to attend a lecture you are still responsible for the material and assignments covered during that class. A reasonable and documented excuse is needed for a missed lab session. If you experience an extended absence due to illness or family emergency, please email me, and we can work out a solution.

Accessibility: The University of Mount Union values disability as an important aspect of diversity and is committed to providing equitable access to learning opportunities for all students. Student Accessibility Services (SAS) is the campus office that collaborates with students with disabilities to provide and/or arrange reasonable accommodations based on appropriate documentation, the nature of the request, and feasibility. If you have, or think you have, a temporary or permanent disability and/or a medical diagnosis in any area, such as physical or mental health, attention, learning, chronic health, or sensory, please contact SAS. The SAS office will confidentially discuss your needs, review your documentation, and determine your eligibility for reasonable accommodations. Accommodations are not retroactive, and the instructor is not obligated to provide accommodations if a student does not request accommodation or provide documentation. Students should contact SAS to request accommodations and discuss them with their instructor as early as possible in the semester. You may contact the SAS office by phone at (330) 823-7372; or via e-mail at studentaccessibility@mountunion.edu.

Academic Honesty: All work you submit with your name on it is expected to be original work. You can consult any outside source, including the internet and AI chats, for help on assignments, but you are not allowed to copy any solutions you find there directly. Additionally, you should be able to thoroughly explain how you arrived at your answer for all work you turn in. If you work closely with other classmates on an assignment, please indicate that the solution results from collaboration and list the names of all students who contributed (this is allowed and encouraged). If it can be proven that you used Chegg, ChatGTP, or another person to solve your homework (i.e., you are copying your solutions directly from these sources or others), or if you are found to be cheating on exams, you will receive a zero for the assignment and be reported for academic dishonesty.

Technology in the Classroom: All electronic devices are allowed in the classroom, provided that you do not use them to distract other students. All devices should be muted and notifications silenced for the class duration. If a device distracts other students, you will be asked to put the device away or leave the classroom.

Communications with the Professor: The best way to ask a question about an assignment is to post it to the class Teams. Even if I do not see the message quickly, other students may be able to help you. If you wish to contact me directly, the best way to reach me is by email or to come by my office. My cell phone number is also provided at the top of the syllabus if you need to contact me quickly.

Grading

Exams: 40%

Your exam score will be calculated as 0.4(A)+0.3(B)+0.2(C)+0.1(D), where A is the exam you scored highest, B is your next highest exam, C is the next highest score, and D your lowest exam score.

Homework: 60%

Each homeworks is worth 10% of your final grade, with the lowest homework being dropped at the end of the course.

Percentage grades can be converted to an A-B scale using the following:

A: 100-94

A-: 93-90

B+: 89-87

B: 86-84

B-: 83-80

C+: 79-77

C: 76-74

C-: 73-70

D+: 69-67

D: 66-64

D-: 63-60

F: 59 and below

Homework

There will be seven homework assigned throughout the semester.

A physical copy of your completed homework is due on their due dates at the start of class. Graded homeworks will be returned within one week of their due date.

All resources are available for your use on the homework (notes, book, other students, internet, chatbots, etc.). However, you must list any external sources (besides notes and book) you use on a question. You are encouraged to collaborate with other students on the homework, but you must list the names of your collaborators.

The homeworks are not timed, but I ask that you record roughly the time taken to answer each question.

Exams

There will be four non-cumulative, take-home exams throughout this course. The release dates and due dates of the exams are listed below. A physical exam copy must be handed to me or left in my office before the listed due date and time.

Each exam will have five questions; four must be answered for full credit. I will base your score on the highest four if you answer all five questions.

You can use your notes and the course textbook for the exams. You are not allowed to use the internet, other resources, or other people. The only internet resource allowed on the exams is Wolfram Alpha or Symlab, and you must state where these were used.

The exams are timed. You can only spend five hours working on the exam, but this can be non-consecutive. You are to record the dates and times you work on the exam on the cover sheet.

You can ask me for assistance on the exam, but you have to trade exam points for assistance. For example, I may offer 3 points to tell you if part (a) of a question is correct. If you take me up on the offer, the highest you can score on the exam is a 97. The more assistance you ask for, the more points I will require.

Late Policy

Late work is only accepted if late days are used. You have five late days that you can use throughout the semester only on the homeworks. Each late day gives you a 24-hour extension on the deadline. Exams must be turned in before the deadline. Situations that require extended deadlines (serious illness, death in the family, etc.) will be handled on a case-by-case basis.

Schedule and Suggested Readings

This schedule is subject to change.

Week 1 (January 8-12, 2024)

Monday: Sections 1.1 - 1.3; Homework #1 Released

Wednesday: Sections 1.4 - 1.6

Friday: Problem Solving Day; Homework #1 Part 1 Due

Week 2 (January 15-18, 2024)

Monday: No Class (MLK Day); Homework #2 Released

Wednesday: Sections 2.1 - 2.2; Homework #1 Part 2 Due

Friday: Section 2.3

Week 3 (January 24-26, 2024)

Monday: Section 2.3

Tuesday: Homework #2 Part 1 Due

Wednesday: Sections 2.4-2.6

Friday:

Week 4 (January 29 - February 2, 2024)

Monday: Sections 2.4-2.6

Tuesday: Homework #2 Part 2 Due

Wednesday: Sections 2.4-2.6;

Friday: Appendix A

Week 5 (February 5-9, 2024)

Monday: Appendix A; Homework #2 Part 3 Due; Appendix A Homework Released

Wednesday: Sections 3.1-3.2; Exam #1 Released; Homework #3 Released;

Friday: Section 3.3

Week 6 (February 12-16, 2024)

Monday: Sections 3.4 - 3.5; Exam #1 Due by 8 a.m.

Wednesday: Section 3.6; Homework #4 Released; Homework #3.1 and Appendix A Homework Due

Friday: Section 4.1

Week 7 (February 19-23, 2024)

Monday: Section 4.2; Homework #3.2 and Appendix A Homework Due

Wednesday: Section 4.2

Friday: Section 4.3

Week 8 (February 26 - March 1, 2024)

Monday: Section 4.3

Wednesday: Problem Solving Day

Friday: No Class (Spring Break)

Week 9 (March 11 - March 15, 2024)

Monday: Section 4.4

Wednesday: Section 4.4

Friday: Section 4.5

Week 10 (March 18-22, 2024)

Monday: Problem Solving Day

Wednesday: Section 5.1 Homework #5 Released; Exam #2 Released

Friday: Section 5.1

Week 11 (March 25-29, 2024)

Monday: Section 5.2; Exam #2 Due by 8 a.m.

Wednesday: Section 5.3

Friday: No Class; Good Friday

Week 12 (April 1-5, 2024)

Monday: Problem Solving Day

Wednesday: Sections 6.1 - 6.3; Homework #6 Released

Friday: Sections 6.4 - 6.5

Week 13 (April 8-12, 2024)

Monday: Sections 6.6 - 6.7

Wednesday: Section 6.8

Friday: Problem Solving Day

Week 14 (April 15-19, 2024)

Monday: Section 7.1; Homework #7 Released

Wednesday: Section 7.1; Exam #3 Released

Friday: Section 7.2

Week 15 (April 22-26, 2024)

Monday: Section 7.2; Exam #3 Due by 8 a.m.

Wednesday: Section 7.3

Friday: Section 7.4

Week 16 (April 29 - May 3, 2024)

Monday: Section 7.5

Wednesday: Problem Solving Day; Exam #4 Released; Last Day of Class

Friday: No Class (Finals); Exam #4 Due by 1 p.m. on May 6