Quantum Mechanics

Real quantum mechanics for talented high schoolers.

Online from anywhere · or in-person in Princeton, NJ

A World Through the Lens of Quantum Mechanics

This course explores the quantum world, one of the four Modern Physics electives in the Physics Lyceum: High School curriculum. It follows the Deep Physicsmodel that runs through the whole SoTS Physics Lyceum.

The course runs on theory, problem-solving sessions, and homework, introducing quantum concepts through concrete optical phenomena.

1. Polarization and the Quantum State

Light through a polarizing filter, and what it tells us about quantum systems. Sunglasses, 3D glasses, camera filters: concrete objects you have held in your hand. Experiments with single photons, polarizers, and the Mach-Zehnder interferometer reveal what a quantum state actually is.

2. Operators and Observables

How physical quantities live in quantum theory. Polarization angle, energy, position, momentum: each becomes an operator acting on states. The values you can measure are the operator's eigenvalues. Some pairs of quantities cannot simultaneously have definite values.

3. Measurement

What actually happens when you measure a quantum system. The Born rule, expectation values, collapse of the state. The proof, from the algebra of non-commuting operators, that uncertainty is a theorem of the algebra, not an experimental limitation.

4. From Photons to Spin

Spin-1/2 and the Stern-Gerlach experiment. Once you understand polarization, spin is the same structure in a different setting: two states, measurement geometry in three dimensions. The 1922 experiment, in which silver atoms split into exactly two beams, becomes the second prototype, and the bridge from photons to electrons, from fields to matter.

5. Angular Momentum and Rotations

Why angular momentum is quantized. Angular momentum operators, the algebra of commutators, and ladder operators. The same algebra that describes a spinning particle determines the orbital structure of atoms.

6. Entanglement and Bell’s Theorem

Two particles in a joint state where you cannot say “particle A is in this state, particle B is in that state.” Only the pair has well-defined properties. You work through Bell’s 1964 proof that no local theory in which particles carry their own definite properties can reproduce quantum predictions. Experiments since the 1970s have tested this. Quantum mechanics has won every time.

The specific topics, and the depth given to each, may shift depending on class priorities and the dynamics of the cohort.

How Quantum Mechanics Is Taught in This Course

We teach quantum mechanics through optical phenomena.

We start with the classic polarization experiments: polarizers, the Mach-Zehnder interferometer, single-photon detection. Concrete enough to picture, strange enough to require quantum theory.

Every conceptual move (superposition, observables, eigenvalue equations, measurement, uncertainty, entanglement) is first made concrete in optical phenomena. Spin, angular momentum, and many-particle systems come later.

What this course does not cover. The course stays in the finite-dimensional setting of polarization and spin, where the structure of quantum mechanics is cleanest. The wave-function treatment of the hydrogen atom, the Schrödinger equation in position space, and the historical photoelectric / Bohr / de Broglie route are by design out of scope. Students who want the wave-function story can read it in a standard introductory text after this course; the operator algebra they learn here is the same algebra that runs underneath it.

Texts and Requirements

Primary text. Mark Beck, Quantum Mechanics: Theory and Experiment (Oxford University Press). We work through chapters 1–8 over one semester.

Prerequisites. Mechanics of Motion and Waves and Oscillations, or equivalent courses elsewhere, plus comfort with complex numbers.

No calculus. This course needs linear algebra rather than calculus, and it develops the linear algebra it needs as it goes.

Schedule, Tuition, and Enrollment

Schedule, tuition, and enrollment
click the line to collapse ψ