Quantum + condensed matter¶

Weeks¶

Week 12¶

Spine: OpenStax University Physics Vol. 3 + David Tong QM

Reading: Vol. 3 Ch. 6 photons/matter waves; Tong Ch. 1 wavefunction/Schrödinger

Know: Use wavefunction/amplitude/probability ideas and understand why classical trajectories fail microscopically.

Reconstruct: Derive de Broglie relation consequences and probability-current/normalization intuition.

Do: Simulate free Gaussian wavepacket spreading and compare to classical particle ensemble.

Defend: What exactly is predicted by a wavefunction?

Gate: Pass: normalization, expectation and qualitative evolution explained without classical hidden trajectory language.

Source: source

Week 13¶

Spine: OpenStax Vol. 3 + Tong QM

Reading: Vol. 3 Ch. 7; Tong Ch. 2-3 1D particle and formalism

Know: Solve simple bound/tunneling systems; use operators/eigenstates/uncertainty and superposition.

Reconstruct: Derive particle-in-box spectrum and commutator-based uncertainty relation.

Do: Numerically solve/tunnel through a 1D barrier and sweep barrier height/width.

Defend: Why is tunneling not a particle 'borrowing energy'?

Gate: Pass: distinguish amplitude, probability and measurement outcome; predict scaling before computation.

Source: source

Week 14¶

Spine: OpenStax Vol. 3

Reading: Ch. 8 Atomic Structure + selected Tong QM hydrogen/angular momentum

Know: Connect quantized structure to atomic spectra, orbitals and selection-rule intuition.

Reconstruct: Derive hydrogen energy scaling and angular-momentum quantization relations at a conceptual/mathematical level.

Do: Fit simple spectral-line data to quantized transition model and quantify model residuals.

Defend: What features of chemistry ultimately originate in quantum structure?

Gate: Pass: explain shell/orbital structure without invoking literal planetary orbits.

Source: source

Week 15¶

Spine: OpenStax Vol. 3 + David Tong Solid State

Reading: Ch. 9 Condensed Matter; Tong Solid State intro/band theory

Know: Understand crystal lattices, free electrons, bands, Fermi surfaces, semiconductors and phonons.

Reconstruct: Derive qualitative band-gap formation from periodic potential and Fermi-Dirac occupation intuition.

Do: Build a simple tight-binding/band-dispersion simulation; compare metal/insulator/semiconductor filling.

Defend: Why can the same atoms form materials with radically different conductivity?

Gate: Pass: connect microscopic structure -> bands -> macroscopic electrical behavior.

Source: source

Week 16¶

Spine: David Tong Solid State + MIT 3.091

Reading: Phonons, magnetism, superconductivity/semiconductor application survey

Know: Connect collective excitations and order to thermal/electronic/magnetic properties; identify what remains unexplained for frontier materials.

Reconstruct: Derive 1D lattice vibration dispersion in simplest chain and explain phonon concept.

Do: Write a falsifiable characterization protocol for a claimed room-temperature superconductor, including transport, field and reproducibility checks.

Defend: What measurements would distinguish superconductivity from a low-resistance artifact?

Gate: Module defense: new-material claim -> quantum mechanism hypotheses + measurement program + uncertainty/fraud/error controls.

Source: source

Exit gate¶

Closed-book: 150 min: wavefunction normalization, box/tunneling, operators/uncertainty, atomic transitions, bands/phonons.

Novel problem: Given an unfamiliar material claim, propose microscopic mechanisms and discriminating measurements.

Artifact: Band/tunneling/lattice simulation plus characterization protocol.

Defend: Defend what is quantum-mechanical, what is material-specific, and what evidence would falsify the claim.

Pass criterion: Pass if mechanism-to-measurement chain is coherent and does not overclaim from one measurement.

Transfer problems¶

Try these before consulting solutions or asking for the complete answer.

1. Wavefunction: Normalize a piecewise wavefunction and compute probability in a region.

2. Box: Derive energy spacing dependence on mass and box size.

3. Tunneling: Quantify sensitivity of tunneling probability to barrier width.

4. Operators: Compute expectation and variance for a small two-state observable.

5. Uncertainty: Construct a wavepacket tradeoff between spatial localization and momentum spread.

6. Atomic spectrum: Infer an energy-level spacing from emitted photon wavelengths.

7. Bands: Build a simple tight-binding dispersion and vary coupling.

8. Semiconductor: Explain qualitatively how doping shifts carrier populations and device behavior.

9. Phonons: Derive dispersion for a 1D spring-mass chain and identify acoustic behavior.

10. Superconductor claim: Design measurements that distinguish zero resistance, Meissner effect, contact artifact and structural transition.

Textbooks¶

See the five-book resource page.