Quantum Mechanics I (PHY 421)

Contact Information

Course Description

An introduction to quantum physics. We explore the mathematical structure of quantum theory, the notion of superposition, and the idea of quantum entanglement (including the Bell inequalities). Our principal examples are based on spin-1/2 systems, the most basic quantum systems.

Learning Objectives

It is expected that students will

  1. describe physical situations using the mathematical language of complex vectors and kets
  2. interpret the results of Stern-Gerlach experiments in terms of quantum theory
  3. apply the postulates of quantum mechanics to specific physical situations
  4. calculate probabilities of measurement outcomes
  5. calculate the future state of a system from its initial state and its Hamiltonian
  6. explain how quantum mechanics violates the limits of local hidden-variable theories

IDEA Objectives

  1. Learning fundamental principles and theories, in particular quantum theory
  2. Gaining factual knowledge and terminology, especially the terminology of kets and operators in which quantum mechanics is expressed
  3. Learning to apply course material to solve problems in quantum mechanics


The textbook for the course is Quantum Processes, Systems, and Information by Benjamin Schumacher and Michael D. Westmoreland, Cambridge University Press, ISBN 978-0-521-87534-9.


There will be three 50-minute exams during the normal class time. There will also be a comprehensive final exam. No computers, cell phones, music players, or any electronic devices with wireless or network capability are allowed during exams. We will discuss whether or not calculators will be needed on exams.


The textbook by Schumacher and Westmoreland contains exercises scattered through the sections and problems at the end of each chapter. I will ask you to read sections of the textbook before coming to class. Please do all of the exercises in each section I assign and bring that work to class. If you cannot complete an exercise, write down a question that helps to uncover where your confusion, misunderstanding, or unawareness lies (or stop by for help). I may or may not collect the daily exercises. The daily exercises will be graded primarily on effort, and will count toward your homework grade for the class.

In addition to the daily exercises, there will be problem sets that are due from time to time. The due dates for the problem sets are listed below. The problem sets will be graded primarily on results (as opposed to effort), and will count toward your homework grade for the class.

You may work together on the daily exercises and on the problems sets, talking about how to solve the problems, but you must write your solutions independently. Do not copy homework solutions from your classmates or from any other source. Copying another person’s homework solutions is an act of cheating and plagiarism. Submitting your own work for the homework will cause you to learn quantum theory. Everything that you write in your homework solutions you should be able to explain to me if I ask. This does not mean that your homework needs to be perfect, only that it must have come from your mind.

If you can’t finish some of the problems before the due date, turn in what you have done. It is still worth trying to do the remaining problems, because they all have a purpose in learning quantum theory. If you know in advance that you will have trouble finishing the homework by the deadline, come and talk to me.

Class Participation

A portion of your grade is determined by class participation. Obviously, attendance is a prerequisite for participation in class. If you attend every class, and participate by asking questions, answering questions, and taking your turn in doing problems at the board, you will have a perfect score for this area. If you need to miss a class, see me in advance if you can, and turn in a written copy of the daily exercises we planned to discuss that day.


Your grade will be determined by a weighted average as indicated in the table below.

Class Participation10%
Final Exam (comprehensive)15%

Your letter grade for the course is determined by the weighted average. The minimum weighted average (out of 100) required for each letter grade is indicated below.


Office Hours

Please feel free to stop by my office any time to chat. I will make a special effort to be in my office during the office hours posted on my door (also listed on my web page). We can also make an appointment to get together if that is convenient for you.

Disabilities Services Syllabus Statement

If you have a physical, medical, psychological, or learning disability that is going to impact your attendance or require accommodation, please let me know. In order to ensure that your learning needs are appropriately met, you will need to provide documentation of your disability or medical condition to the Director of Disability Services. The Office of Disability Services will then provide a letter of verification of disability that describes the accommodations needed for this class. This office is located in the Humanities Building, room 04, and the Director may be reached by phone at 717-867-6071.

Academic Honesty

Lebanon Valley College’s Academic Honesty Policy is written in the college Catalog, and at http://www.lvc.edu/catalog/acad-reg-procedures.aspx. This code asks each student to do their own work in their own words:

Lebanon Valley College expects its students to uphold the principles of academic honesty. Violations of these principles will not be tolerated. Students shall neither hinder nor unfairly assist the efforts of other students to complete their work. All individual work that a student produces and submits as a course assignment must be the student’s own. Cheating and plagiarism are acts of academic dishonesty. Cheating is an act that deceives or defrauds. It includes, but is not limited to, looking at another’s exam or quiz, using unauthorized materials during an exam or quiz, colluding on assignments without the permission or knowledge of the instructor, and furnishing false information for the purpose of receiving special consideration, such as postponement of an exam, essay, quiz, or deadline of an oral presentation. Plagiarism is the act of submitting as one’s own the work (the words, ideas, images, or compositions) of another person or persons without accurate attribution. Plagiarism can manifest itself in various ways: it can arise from sloppy, inaccurate note-taking; it can emerge as the incomplete or incompetent citation of resources; it can take the form of the wholesale submission of another person’s work as one’s own, whether from an online, oral or printed source. The seriousness of an instance of plagiarism—its moral character as an act of academic dishonesty—normally depends upon the extent to which a student intends to deceive and mislead the reader as to the authorship of the work in question. Initially, the instructor will make this determination.

Once academically dishonest work has been submitted, the instructor shall report the suspected incidence to the associate dean of the faculty. At the moment the work has been submitted, the student involved forfeits the right to withdraw from the course or to change his or her course status in any way. The College’s expectations and the measures it will apply to support and enforce those expectations are outlined below.

For the first offense of academic dishonesty, the faculty member has the option of implementing whatever grade-related penalty he or she deems appropriate, up to and including failure in the course. The associate dean of the faculty shall send the student a letter of warning, explaining the policy regarding further offenses and the appeal process.

Class Schedule

DateTopicRead before classHand in
01/20Complex numbersQRGLAQM Sec. 1
01/22Interferometer2.1 (Ex. 2.1–2.10)
01/25Photon2.1 (Ex. 2.11–2.17)PS 1
01/27Spin 1/22.2
02/01Two-level atoms2.3
02/03Time evolutionPS 2
02/08Ch. 2 summary
02/10Hilbert space3.1 (Ex. 3.1–3.10)PS 3
02/12Operators3.2 (Ex. 3.11–3.20)
02/15Exam 1 (Ch. 2)
02/17Operators3.2 (Ex. 3.21–3.28)
02/22Adjoints3.4 (Ex. 3.34–3.42)PS 4
02/24Eigenvalues3.5 (Ex. 3.43–3.49)
02/26Eigenvectors3.5 (Ex. 3.50–3.56)
03/02Cryptography4.3–4.4PS 5
03/07Spring vacation
03/09Spring vacation
03/11Spring vacation
03/16Schrodinger eqn.5.2
03/18Clocks5.3, 5.4 (Ex. 5.12–5.16)
03/21Symmetries5.4 (Ex. 5.17–5.22)
03/23Composite systems6.1 (Ex. 6.1–6.6)PS 6
03/25Easter vacation
03/28Easter vacation
03/30Composite systems6.1 (Ex. 6.7–6.11)
04/01Exam 2 (Ch. 3, 4, 5)
04/06A 4pi world6.3
04/08Conditional states6.4
04/11Bell’s theorem6.5, 6.6, 6.7PS 7
04/13Particle in space10.1
04/15Continuous observables10.2 (Ex. 10.6–10.11)
04/18Wave packets10.3, 10.4
04/20Continuous observables10.2 (Ex. 10.12–10.17)
04/22ValleyFest, no class
04/25More space10.5, 10.6PS 8
04/27Dynamics in 1-D11.1, 11.2
04/29Exam 3 (Ch. 6, 10)
05/02Particle in a box11.3, 11.4
05/04Quantum Billiards11.5PS 9