Quantum Mechanics: High School, Princeton
Real quantum mechanics, taught through optical phenomena. For talented high schoolers.
A World Through the Lens of Quantum Mechanics
At small scales, nature does things classical physics has no answer for.
Send a beam of silver atoms through a magnetic field. Classical physics predicts a continuous smear, since the atomic magnets point in every direction. The screen shows two sharp spots. Nothing between them.
Classically, a measurement reveals what was already there: a thermometer reads a temperature the thing had before. In quantum mechanics, the measurement changes the state. The value you read was not waiting to be found. It was produced.
Classically, a particle has all its properties at every moment, and better instruments measure them more precisely. In quantum mechanics, certain pairs of properties cannot both have definite values at once. The theory says no such state exists.
Classically, distant objects are independent, or correlated only through their shared past or signals between them. Two quantum particles, prepared together and separated by light-years, stay correlated in ways neither past nor signal can explain.
Quantum mechanics is the theory that makes sense of all of this. The most precisely tested theory in the history of physics.
This course teaches you what physicists actually know about it. With precision.
You will:
- Use a quantum state to predict what an experiment measures.
- Derive the uncertainty principle from the algebra of non-commuting operators.
- Compute the predictions of quantum mechanics for entangled particles.
- Prove Bell’s theorem yourself.
By the end, you will think about quantum mechanics the way a physicist thinks about it.
What You Will Actually Understand
By the end of the course, you will understand six core ideas of quantum mechanics.
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: the single fact that separates quantum from classical physics.
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. The conceptual heart of quantum mechanics.
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. Derived from rotational symmetry, using the algebra of angular momentum operators and ladder operators. The same algebra that describes a spinning particle determines the orbital structure of atoms.
6. Entanglement and Bell’s Theorem
The deepest result in twentieth-century physics. 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. The destination, a working understanding of the conceptual core of quantum mechanics, stays the same.
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.
Primary text: Mark Beck, Quantum Mechanics: Theory and Experiment (Oxford University Press). We work through chapters 1–8 over one semester. Students purchase their own copy; the book is not included in tuition.
Schedule, Pricing & Enrollment
Formats: Fall, Spring, and Summer semesters.
Schedule, format, tuition, refund policy, and transcripts apply to every Lyceum course. They live on the Physics Lyceum: High School overview.
To enroll, schedule a call. We confirm fit, prerequisites, and the right semester.
Part of the SoTS Physics Lyceum
Quantum Mechanics is the most advanced of eight semester-long physics courses in the SoTS Physics Lyceum: a multi-year curriculum in Princeton, NJ.
Mechanics of motion. Mechanics of bodies and fluids. Waves and oscillations. Thermodynamics. Electricity and magnetism. Optics and atomic structure. Special Relativity. Quantum mechanics.
The Lyceum is built on the Deep Physics methodology.