“I think I can safely say that nobody understands quantum mechanics.” — Richard Feynman
The Bloch equations describe how a magnetic moment precesses, relaxes, and responds to resonant driving fields. They are the foundation of everything that follows in the magnetometer: optical pumping, Larmor precession, signal demodulation, and state estimation all reduce to solving these equations under different conditions.
What This Lesson Covers
Starting from a single spin-½ in a static magnetic field, the lesson builds up to the full Bloch vector equations through:
- The Larmor frequency — why spins precess, and at what rate
- The density matrix — parameterising the quantum state of an ensemble
- The Bloch vector — three real numbers that capture everything observable
- Relaxation — T₁ (longitudinal) and T₂ (transverse) decay
- Optical pumping — preparing the spin state with circularly polarised light
Each concept is implemented in Python, Haskell, and C++ simultaneously. The three implementations must agree on the physics — a discrepancy between them means someone has misunderstood something.
Pedagogical Cadenzas
The lesson includes self-contained “cadenza” modules for prerequisite concepts that a first-year graduate student might need to review: angular momentum, the Pauli matrices, density operators, and the rotating frame.
Content pipeline: This page summarises Lesson 00. The full lesson with derivations, code blocks, and exercises lives in the source repository and will be exported here as the ox-hugo pipeline matures.
Source: modules/mayapramana/lessons/00-bloch-equations/concept.org (885 lines, ~34 KB)