Unofficial Course Title: Quantum
Spring Semester (Terms 4 & 5) 2026, Deep Springs College, Prof. Brian Hill
Directed Study Students: Lucinda Bean (DS 25) and Grisha London (DS 25)
Course meeting times: 9:30-10:55am, Mo/Th
The Quantum Mechanics DS Proposal will serve as our preliminary syllabus.
Detailed daily schedules will be kept retrospectively:
We will study quantum mechanics, starting with Spin 1/2 and Spin 1 systems, and conclude with Schrodingers Equation and some of its solutions, following Feynman, and with supplementary material from Moore when Feynman gets too advanced for an introductory course.
Normally one does not get to study quantum mechanics in the depth we will go into until the junior year as a physics major. To get to this level of quantum mechanics so quickly, we are short-circuiting past electromagnetism. A substantial cost of this is that you have not even encountered electromagnetic waves! So to understand quantum-mechanical waves we will first immerse ourselves in other, simple examples of waves. We also have to introduce you to complex numbers, which is normally done in a semester-long sophomore level mathematics course. We will learn the essential results from complex numbers following the first chapter of Churchill, Brown, and Verhey. The upshot is that this is an extremely ambitious course for first-years to take in their spring semester, who only have classical mechanics and calculus taken previously.
Nonetheless, by the end of our quantum mechanics studies, you will be able to do probabilistic calculations using the strange mixture of deterministic time evolution punctuated by non-deterministic measurement events. You will understand how systems with 2, 3, 6, and an infinite number of states. Following the propagation of particles through a crystal lattice, which has wave solutions, we will immerse ourselves in the Schrodinger equation as our final topic.
In summary, in this course you will encounter behaviors and theories so strange and wonderful that no human could have thought them up. Instead, nature rubbed the behaviors in the faces of physicists, who eventually, even miraculously, in the early 20th century, were able to understand and articulate what nature was showing them.