Fundamentals of Physics II: E&M, Optics, and 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. Be aware that quantum mechanics is the final act of a broader course: the first eighteen lectures cover electromagnetism and optics, and the last seven lectures (Quantum Mechanics I through VII) develop quantum theory. The lectures can be followed as a standalone resource, and learners interested only in quantum mechanics can jump straight to lecture 19.

What you’ll learn

The quantum portion of the course opens by examining the key experiments that made quantum mechanics necessary and the wave-particle duality they reveal, establishing the empirical stakes before the theory is introduced.

Wave functions are then developed as the fundamental objects of quantum theory. The Schrodinger equation is introduced and analyzed, with the particle in a box worked through carefully and with attention to the physical meaning of each result rather than just its mathematical form. The uncertainty principle and its physical content are examined along the way.

The later lectures cover measurement theory and states of definite energy, the time-dependent Schrodinger equation, and a closing summary of the postulates of quantum mechanics with selected special topics. Before all of this, the first eighteen lectures give a full treatment of electrostatics, circuits, magnetism, Maxwell’s equations, and geometrical and wave optics, valuable background in its own right.

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.