# Resources — Supplementary Textbooks > A shelf, not a spine. This section holds self-contained lesson sequences built alongside outside > textbooks whose treatment of a topic is worth having in full — an alternative route up the same > mountain, for when the program's own path leaves you wanting a second explanation. Nothing here is > a prerequisite for anything in Terms 0–5; everything here is optional, and everything here has > somewhere in the main program it plugs into. **Estimated time:** ~32 hours · **Lessons:** 8 across 2 courses **Prerequisites:** undergraduate classical mechanics and the program's assumed background. **Position in the program:** entirely optional. Course R.1 pairs naturally with the [Pre-Term](../pre-term-wave-mechanics/README.md) and with [Term 1](../term-1-quantum-mechanics/README.md), and can be read before, during, or after either. Course R.2 continues directly from R.1 and reaches into [Term 1.4](../term-1-quantum-mechanics/README.md) (entanglement) and Term 4 (hardware). --- ## Why this section exists The main program enters quantum mechanics through its axioms, and the [Pre-Term](../pre-term-wave-mechanics/README.md) enters through wave mechanics. There is a third door, and some people find it the best one: start from a single experiment, follow it until the classical description breaks, and let the formalism be forced on you rather than announced. That is the approach James K. Freericks takes in *Quantum Mechanics Done Right*, whose opening chapter builds the entire conceptual apparatus of measurement — states, the Born rule, incompatible observables, projection — from the Stern-Gerlach experiment and nothing else. Course R.1 covers the same ground as that chapter, in this program's notation and at this program's level, with original derivations, worked examples, exercises, and code. Read it if you want the *experimental* motivation for the postulates before you meet them axiomatically in Term 1, or if the phrase "the measurement collapses the state" has never quite sat right and you would like to see exactly which observation forces it. Course R.2 continues into that book's second chapter, and it is where the door R.1 deliberately left open gets shut. It builds an apparatus that provably *does nothing* — the Stern-Gerlach analyzer loop — and then uses the difference between "does nothing" and "does something" to reach interaction-free measurement, the quantitative form of complementarity, quantum erasure, and finally a Bell experiment that refutes every local hidden-variable theory by counting to nine. The chapter closes somewhere completely different: nuclear magnetic resonance, where the same precession that made the 1922 magnet work becomes the instrument behind every MRI scanner in every hospital. ## Course Map ```mermaid flowchart TD R11["R.1.1 Classical Stern-Gerlach
(what physics predicted)"] R12["R.1.2 Quantum Stern-Gerlach
(what actually happened)"] R13["R.1.3 Probability
(the language of the answer)"] R14["R.1.4 Conundrum of Projections
(why it cannot be classical)"] R21["R.2.1 The Analyzer Loop
(a device that does nothing)"] R22["R.2.2 Complementarity
(which-way vs interference)"] R23["R.2.3 EPR & Bell
(local realism refuted)"] R24["R.2.4 NMR & Imaging
(precession as an instrument)"] R11 --> R12 --> R13 --> R14 R14 --> R21 --> R22 --> R23 R11 -.-> R24 PRE["Pre-Term P.6.3
Stern-Gerlach & Spin"] -.-> R11 R14 --> T1["→ Term 1.3: Measurement"] R23 --> BELL["→ Term 1.4.3: Nonlocality & CHSH"] R24 --> T4["→ Term 4: Hardware & pulse control"] ``` **Reading order.** R.1's four lessons are strictly sequential — each one's punchline is the next one's premise — and R.2.1 through R.2.3 continue that same chain. R.2.4 is the exception: it needs only the Larmor precession of R.1.1 and can be read at any point, including on its own. --- ## Courses & Lessons ### Course R.1 — Introduction to the Quantum World (Freericks) `c01-freericks-intro-quantum-world/` A first pass at quantum mechanics through one experiment, following the arc of [Fre] Ch. 1. 1. [Classical Stern-Gerlach Experiment](c01-freericks-intro-quantum-world/01-classical-stern-gerlach.md) — dipoles in field gradients, precession vs libration, and the continuous band classical physics predicts. 2. [Quantum Stern-Gerlach Experiment](c01-freericks-intro-quantum-world/02-quantum-stern-gerlach.md) — two spots, the analyzer abstraction, five cascade experiments, and the $\cos^2(\theta/2)$ law. 3. [Probability in the Quantum World](c01-freericks-intro-quantum-world/03-probability-quantum-world.md) — compound probabilities, shot noise, and why amplitudes rather than probabilities are what add. 4. [The Conundrum of Projections](c01-freericks-intro-quantum-world/04-conundrum-of-projections.md) — the impossibility proof, the projection postulate, incompatible observables, and the measurement staircase. ### Course R.2 — Advanced Quantum Mechanics of Spin (Freericks) `c02-freericks-advanced-spin/` The same experiment pushed until it breaks local realism, following the arc of [Fre] Ch. 2. 1. [The Analyzer Loop](c02-freericks-advanced-spin/01-analyzer-loop.md) — an apparatus that provably does nothing, gate configurations, partial which-way detectors, and interaction-free measurement. 2. [Complementarity & Delayed Choice](c02-freericks-advanced-spin/02-complementarity-delayed-choice.md) — which-way information as a quantitative trade-off, $D^2 + V^2 \le 1$, quantum erasure, and Wheeler's refutation of the conspiracy theory. 3. [Einstein, Podolsky, Rosen & Bell](c02-freericks-advanced-spin/03-epr-and-bell.md) — the singlet, the EPR argument, no-communication, instruction sets, and the three-setting Bell test. 4. [Nuclear Magnetic Resonance & Imaging](c02-freericks-advanced-spin/04-nuclear-magnetic-resonance.md) — resonance and the rotating frame, pulse design, chemical shift, spin echo, and how an MRI machine turns frequency into position. --- ## Course Learning Outcomes By the end of Course R.1 you will be able to: 1. Derive the **classical** prediction for the Stern-Gerlach experiment and explain why the apparatus requires both a field gradient and a rotor carrying angular momentum. 2. State the results of the five cascaded-analyzer experiments and compute any of their outcome probabilities from the $\cos^2(\theta/2)$ law. 3. Build the spin-$\tfrac12$ state space $\mathbb{C}^2$ from the experimental facts alone, and apply the **Born rule** to it. 4. Distinguish classical randomness from quantum indeterminacy, and compute the shot budget needed to test a quantum probability to a stated precision. 5. Prove that no assignment of pre-existing classical moment vectors reproduces the observations, and state precisely what that argument does and does not rule out. 6. Express measurements as **projectors**, compute sequential-measurement probabilities, and connect incompatibility to the non-vanishing of $[S_z, S_x]$. By the end of Course R.2 you will be able to: 1. Prove that a recombining **analyzer loop** acts as the identity, and predict the output of any cascade of loops with arbitrary gates closed. 2. Explain how adding a blocker can *increase* throughput, and compute the efficiency of an **interaction-free measurement**. 3. Derive the duality relation $D^2 + V^2 \le 1$ from a spin–marker entangled state, and use the partial trace to show that no human observer enters the prediction. 4. Analyze **quantum erasure** and delayed choice without invoking backward causation, and rule out any theory in which the unwatched atom travels a single definite branch. 5. Compute both predictions for a three-setting **Bell experiment** — the quantum $\tfrac12$ and the local-realist bound $\ge\tfrac59$ — and explain why a four-setting version cannot decide anything. 6. Construct the **rotating frame**, design $\pi/2$ and $\pi$ pulses from hardware numbers, and explain what an MRI machine actually measures. --- ## Where this plugs into the program | This course | Continues in | | -------------------------- | --------------------------------------------------------------------------------------------------------------------- | | Spin-$\tfrac12$ as $\mathbb{C}^2$ | [1.2.1 The Qubit](../term-1-quantum-mechanics/c02-qubits-bloch/01-the-qubit.md) | | The half-angle law | [1.2.2 The Bloch Sphere](../term-1-quantum-mechanics/c02-qubits-bloch/02-bloch-sphere.md) | | The projection postulate | [1.3.1 Projective Measurement](../term-1-quantum-mechanics/c03-measurement/01-projective-measurement.md) | | Uncertainty and $[S_z,S_x]$ | [1.3.2 Expectation & Uncertainty](../term-1-quantum-mechanics/c03-measurement/02-expectation-uncertainty.md) | | The open hidden-variable question | [1.4.3 Nonlocality & CHSH](../term-1-quantum-mechanics/c04-entanglement/03-nonlocality-chsh.md) | | The experiment itself | [P.6.3 Magnetic Moments, Stern–Gerlach & Spin](../pre-term-wave-mechanics/c06-angular-momentum/03-magnetic-fields-stern-gerlach-spin.md) | | Two-atom states and entanglement | [1.4.1 Multi-Qubit States](../term-1-quantum-mechanics/c04-entanglement/01-multi-qubit-states.md) and [1.4.2 Bell States](../term-1-quantum-mechanics/c04-entanglement/02-bell-states.md) | | The Bell experiment, in operator form | [1.4.3 Nonlocality & CHSH](../term-1-quantum-mechanics/c04-entanglement/03-nonlocality-chsh.md) | | Which-way markers and decoherence | [1.5.2 Partial Trace & Reduced States](../term-1-quantum-mechanics/c05-density-matrices/02-partial-trace-reduced-states.md) | | Resonance and pulse control | [1.6.2 Two-Level Dynamics & Rabi Oscillations](../term-1-quantum-mechanics/c06-dynamics/02-two-level-rabi.md) | | NMR relaxation, $T_1$ and $T_2$ | [Open Systems & Decoherence](../term-4-noise-hardware/c01-open-systems/01-open-systems-decoherence.md) *(Term 4, planned)* | | Spin qubits and pulse sequences | [Superconducting Qubits](../term-4-noise-hardware/c04-hardware/01-superconducting-qubits.md) *(Term 4, planned)* | --- ## Source & Attribution Courses R.1 and R.2 cover the same material as Chapters 1 and 2 of J. K. Freericks, *Quantum Mechanics Done Right* (Springer, 2026), cited throughout as **[Fre]**. The lessons are **original writing** — explanations, derivations, worked examples, exercises, and code are this program's own, in this program's notation and conventions. Section citations such as `[Fre, §1.2]` point you to the corresponding discussion in the book, which is well worth reading in its own right and is available under a Creative Commons licence. --- ← Back to [Program Index](../README.md) · Begin: [R.1.1 Classical Stern-Gerlach Experiment](c01-freericks-intro-quantum-world/01-classical-stern-gerlach.md) · Or jump to [R.2.1 The Analyzer Loop](c02-freericks-advanced-spin/01-analyzer-loop.md) →