Quantum Mechanics
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Quantum Mechanics

PHYS 5115, Fall 2018

Instructor: Professor Jim Halverson

E-mail: j.halverson@northeastern.edu

Phone: 617-373-2957

Office Hours: MW 8:00-9:30

Grader: Jiahua Tian, tian.jiah@husky.neu.edu

"Quantum mechanics is the description of the behavior of matter and light in all its details and, in particular, of the happenings on an atomic scale. Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen." - Richard Feynman. See here for more.

"The universe is under no obligation to make sense to you." - Neil DeGrasse Tyson.

Course Information

Course Schedule: MW 2:50-4:30

Course Location: Ryder 159

Description: Lays out the basic axioms of quantum mechanics, and the complementarity between the wave function and matrix mechanics approach to quantum systems. Considers systems of spins in static and dynamical settings, deriving the algebra for addition of angular momenta. Introduces the notion of time evolution and coherent states/wave packets. Demonstrates the solution to numerous one and three-dimensional problems, including the harmonic oscillator, Coulomb potential, and finite/infinite potential wells. Extends these results to new potentials via the use of perturbation theory and the variational method. Some advanced topics will be covered.

Course Goals:

  • Understand the relation between physical observables and quantum operators.
  • To appreciate the need for complex quantum states, and how phases are related to physically meaningful quantities.
  • To develop familiarity in solving eigenvalue problems.
  • To be able to understand the time evolution of dynamical systems.
  • To become familiar with the use of raising and lowering operators in various systems.
  • To learn basic techniques in the solving of differential equations relevant to quantum systems in one and three dimensions.
  • To become adept at the use of approximation methods such as perturbation theory and the variational method.
  • To expose students to topical advanced subjects such as groups and symmetries, entanglement, decoherence and quantum information theory.

Resources: The textbook we will use is A Modern Approach to Quantum Mechanics (2nd ed.) by John S. Townsend. Not all material covered in lectures will be found in the textbook, so attendance at lectures is strongly encouraged. It is assumed that you will have read the relevant textbook passages before attending the lectures.

Homework: Problem sets will be assigned each week. They will be collected at the start of the Thursday lecture, and during that time the problems for the next week will be assigned, one week before they are due. Late assignments will not be collected under any circumstance. Instead, your lowest homework score will be dropped; if it is a missed assignment it is your responsibility to learn the material, since it may appear on the midterm or final exam. You may discuss the assignments with your classmates, but the work you submit must be your own.

Midterm: There will be an in-class midterm that may test any of the material from homework or class up to that date.

Final Exam: There will be a take home final exam, distributed electronically to the class on TBD. All final exams must be returned to my office, Dana 226, by 5 PM EST on TBD. If I am not in my office, you may put it under my closed door, but you must send me an e-mail alerting me and telling me the time of delivery. The exam is your work only.

Grading: Your final grade will be determined based on your performance on the homework assignments, midterm, and the final exam. The scoring breakdown is as follows: homework 50%, midterm 20%, final 30%.

Final Letter Grade: Your course grade will be determined both by your overall weighted total score, with the weights given above under “Grading”. The following table indicates ‘target’ overall score ranges corresponding to various final course grades

  • A = 93-100%
  • A- = 88-92%
  • B+ = 84-88%
  • B = 78-84%
  • B- = 74-78%
  • C+ = 70-74%
  • C = 65-70%
  • C- = 60-65%

Since exams and assignments can vary slightly in difficulty from semester to semester, the actual score ranges may be adjusted slightly downward from those given in the table. That is, if your final percentage falls in one of the above ranges, you will receive the associated letter grade or higher. Under extreme circumstances the ranges may be shifted in the opposite direction, but this will be announced explicitly in class before April 1.

Course Material

An approximiate outline of the lectures is given below.

  • Lecture 1. Superposition
  • Lecture 2. Quantum states
  • Lecture 3. Rotations and basis change
  • Lecture 4. Matrix representation of operators
  • Lecture 5. Angular momentum
  • Lecture 6. Eigenvalue problems and uncertainty relations
  • Lecture 7. Time evolution
  • Lecture 8. Example: ammonia molecule
  • Lecture 9. Addition of angular momenta
  • Lecture 10. Wave functions and spatial translation
  • Lecture 11. Wave packets; 1D potentials
  • Lecture 12. Scattering in 1D; simple harmonic oscillator
  • Lecture 13. Harmonic oscillator (HO)
  • Lecture 14. Time dependence of HO and coherent states
  • Lecture 15. Schrodinger equation in three dimensions
  • Lecture 16. Angular solutions to central potentials
  • Lecture 17. Radial solutions: Coulomb potential; finite well
  • Lecture 18. Radial solutions: infinite well, 3D HO
  • Lecture 19. Perturbation theory
  • Lecture 20. Stark effect; relativistic corrections to hydrogen atom
  • Lecture 21. Spin-orbit coupling; Zeeman effect
  • Lecture 22. Variational method; cross-sections
  • Lecture 23. Advanced topics 1.
  • Lecture 24. Advanced topics 2.

Comments and Recommendations

Study Groups: You are strongly encouraged to form small groups to work together on the homework. This will aid in the learning process, but note that it is very important that you participate in finding the solutions, and you present your own write-up. Doing so is critical for learning the material and doing well on the midterm and final, since the latter two must be entirely your own work.

Help: If you have trouble with the homework, seek help immediately; do not fall behind in the course. You have several places to go for help: your lecturer (after class or during office hours); the Physics Workshop in 300 Churchill near the physics labs (a schedule should be posted near 111 Dana by the second week of class). There is also peer tutoring available. See here for more details.

Academic Integrity and Misconduct: Be sure to review Northeastern Academic Integrity policies, which are here.

Appropriate disciplinary action, potentially including failing the student, will be taken in the event of cheating, plagiarism, dishonesty, or other academic misconduct. Since students in this course are often encouraged to work in teams, some specific remarks are in order. It is not considered cheating if you:

  • Work together on homework assignments, as long as you each work out and submit your own final answers.
  • Get help from professors, physics workshop, tutors, etc. on the homework assignments.
  • Work together on preparing for exams. It is considered cheating if you:
  • Submit work done by others (without your participation) as your own.
  • Copy work on exams.

In addition, please review the relevant College of Science Academic Course Policies