Fundamentals of Physics II: Quantum Mechanics (Yale)

R. Shankar’s quantum mechanics lectures are among the most admired physics teaching resources available online. Shankar is the author of one of the standard graduate-level quantum mechanics textbooks, and that depth of understanding is evident in how he constructs his explanations. He has a gift for making the conceptually strange aspects of quantum mechanics feel inevitable rather than arbitrary, which is a rare quality in a subject that most students find deeply counterintuitive at first encounter.

These Yale Open Courses lectures form the second half of a two-semester undergraduate physics sequence, PHYS 201. They can be followed as a standalone resource, though students unfamiliar with Shankar’s classical mechanics treatment may want to review the relevant material from his textbook alongside the lectures.

What you’ll learn

The course opens by examining the failures of classical physics that made quantum mechanics necessary. The photoelectric effect and the discrete spectra of atomic emission are used as the motivating puzzles that classical theory cannot resolve, establishing the empirical stakes before the theory is introduced.

Wave functions are developed as the fundamental objects of quantum theory. The Schrodinger equation is derived and analyzed for a series of canonical potentials: the infinite square well, the finite square well, and the harmonic oscillator. Solutions are worked through carefully, with attention to the physical meaning of each result rather than just its mathematical form. The uncertainty principle is derived from first principles using commutator algebra, and its physical content is examined at length.

The later lectures introduce the algebraic method for the quantum harmonic oscillator, using raising and lowering operators to derive the energy spectrum and wave functions without solving a differential equation. Angular momentum is treated in full generality, including the quantization of orbital angular momentum and the introduction of spin. The course closes with quantum measurement, the role of the observer, and an honest engagement with the conceptual foundations of the theory, including the measurement problem.

Who is this for

This course is ideal for physics undergraduates working through their first serious quantum mechanics course, for students in chemistry, materials science, or engineering who want a rigorous physical foundation, and for mathematically confident self-learners who want to understand quantum mechanics at the level a physicist would. It also works well as a conceptually clear refresher for those who encountered quantum mechanics previously but want to revisit the foundations.

Prerequisites

A year of undergraduate calculus-based physics is the practical minimum. Students should be comfortable with differential equations, complex numbers, and linear algebra before beginning. Prior exposure to classical waves and optics is helpful but not strictly required. No programming experience is needed; this is a purely theoretical course.