Quantum Fundamentals

Course Credits

PH 425: Paradigms in Physics: Quantum Fundamentals meets 7 hours per week (MWF for 1 hour, TR for 2 hours) for five weeks for a total of 3 credits.

Prerequisites, Co-requisites and Enforced Prerequisites

Prereq: PH 213
Coreq: MTH 341

Office Hours

Learning Resources

A complete list of required texts and other resources for the the entire year of Paradigms courses can be found on the Paradigms website. For this course, the required text is McIntyre (McI). 

Course Content

The “Quantum Fundamentals” course is built upon the quantum mechanical two state system. The first of the Quantum Paradigms, this course introduces students to quantum mechanics by beginning with the postulates of quantum mechanics and how the postulates are used to gather information about quantum mechanical systems. The common spin-up and spin-down state vectors with x,y, and z-orientation will be derived, and the general state vector |ψ(θ,ϕ)⟩ will also be introduced. Throughout the class, students perform several simulated experiments with virtual Stern-Gerlach devices and interpret their results. Operators that correspond to physical observables in quantum experimentation are then presented; students will learn in particular about spin operators, projection operators, the density operator, and the Hamiltonian. Important physical relations among these quantum operators will also be made using the commutators, uncertainty relations, and expectation values. Spin 1 systems are also introduced as an additional context for exploring and interpreting Stern-Gerlach experiments. The time evolution of quantum states using the Schrodinger Equation will also be explored to investigate time dependence in probabilities, uncertainties, and expectation values. The course ends with and introduction to wavefunctions and solving the Schrödinger Equation for one-dimensional potentials.

Student Learning Outcomes

Students shall be able to:

• Express quantum states and perform quantum calculations in matrix, Dirac, or wavefunction notation (as appropriate)
• Express a quantum state as a linear combination of eigenstates and interpret the expansion coefficients as probability amplitudes  
• Use the Schroedinger equation to determine the time evolution of a spin quantum system or particle in an infinite 1D potential well  
• Calculate energy eigenvalues and eigenstates from a Hamiltonian provided in matrix form, or for a function in the case of the bound states of an infinite 1D potential well
• Use commutation relations to identify an uncertainty relation between observables
• Qualitatively sketch a wavefunction in a 1D potential and describe important features such as boundary conditions, oscillatory/exponential behavior, amplitude, and wavenumber

Evaluation of Student Performance

• 50% required Homework and other assignments.
• 10% Quizzes - Mondays in class
• 40% Exam (Monday, March 16 in Wngr 212).

Additional Information about Homework

• Practice problems provide simple examples for you to check whether or not you understand the material as you go along.  They will not be graded.  Sometimes solutions will be posted.  At a minimum, you should read each practice problem and make sure that you know how to do it. If you can't, ask for help!
• Required problems will be graded.  Solutions will be posted online.  Assignments turned in after solutions are posted can earn at most 50% of the total points.  Very late assignments will earn less.  It is a good idea to turn in what you have done by the due date, and, if necessary, the rest later. Please consult the instructor for special circumstances.
• In 400/500 level classes, some of the required problems and probably one problem on the final exam will be marked as "Challenge" problems.   500-level students are required to do these Challenge problems.  400-level students are not necessarily expected to do them.  However, those students who hope to get an A are encouraged to do so.  While it may be possible for a 400-level student to get an A without doing any Challenge problems, it may be difficult.  (In PH 320, they are optional and don't count for anything--just fun.) Grading of the Challenge problems will be quite strict; we won't even look at them unless they seem to be clearly written, coherent, complete, and essentially correct.

Statement of Expectations for Student Conduct

Students will be expected to abide by all university rules regarding student conduct and academic honesty, in particular, see:  https://beav.es/codeofconduct 

Additional Ground Rules

Science is inherently a social and collaborative effort, each scientist building on the work of others. Nevertheless, each student must ultimately be responsible for his or her own education. Therefore, you will be expected to abide by a number of Ground Rules:

1. We strongly encourage students to work with each other, more advanced students, the TA, and the professor, on assignments. However, each student is expected to turn in assignments that have been independently written up. In other words, the final synthesis must be entirely your own. This applies also to, and especially to, computer generated worksheets. If you work with someone on a computer project, do not get locked into writing the solution together. You will end up turning in the sameassignment.
2. Homework solutions from previous years are very strictly off limits. You are on your honor not to use them, and not to share your homework solutions with other students. Allow faculty to use their time interacting with you, rather than continually thinking up new assignments. Besides, if you don't do the work yourself, it will show up very clearly on exams later. Likewise, the solutions are for your use only. You may make one copy and keep it in your personal files.
3. Sources must be appropriately documented. If you find a homework problem worked out somewhere (other than homework solutions from previous years), you may certainly use that resource, just make sure you reference it properly. If someone else helps you solve a problem, reference that too. In a research paper, the appropriate reference would be:    Jane Doe, (private communication).
4. Plagiarism – representing someone else’s work as your own – is unethical, but collaboration and exchange of ideas is healthy. You can avoid having collaborative efforts take on the look of plagiarism by acknowledging sources and by writing up your work independently.
5. If you find that you have worked on a problem for 1/2 hour without making any forward progress, it would be a good idea to stop and seek help.

Reach Out for Success

University students encounter setbacks from time to time. If you encounter difficulties and need assistance, it’s important to reach out. Consider discussing the situation with an instructor or academic advisor. Learn about resources that assist with wellness and academic success atoregonstate.edu/ReachOut. If you are in immediate crisis, please contact the Crisis Text Line by texting OREGON to 741-741 or call the National Suicide Prevention Lifeline at 1-800-273-TALK (8255)

Statement Regarding Students with Disabilities

Accommodations for students with disabilities are determined and approved by Disability Access Services (DAS). If you, as a student, believe you are eligible for accommodations but have not obtained approval please contact DAS immediately at 541-737-4098 or at http://ds.oregonstate.edu. DAS notifies students and faculty members of approved academic accommodations and coordinates implementation of those accommodations. While not required, students and faculty members are encouraged to discuss details of the implementation of individual accommodations.

Student Evaluation of Courses 

The online Student Evaluation of Teaching system opens to students the Wednesday of week 8 and closes the Sunday before Finals Week. Students will receive notification, instructions and the link through their ONID. They may also log into the system via Online Services. Course evaluation results are extremely important and used to help improve courses and the learning experience of future students. Responses are anonymous (unless a student chooses to “sign” their comments agreeing to relinquish anonymity) and unavailable to instructors until after grades have been posted. The results of scaled questions and signed comments go to both the instructor and their unit head/supervisor.  Anonymous (unsigned) comments go to the instructor only.