Computational Physics

Python pathway

Programming Foundations / Practice rooms / Track curriculum and enrollment

1. Quantum States & Measurement

   Represent normalized complex qubit states, preserve relative phase, compute Born probabilities and observable expectations, and simulate a seeded measurement experiment. Compare sampled counts with predictions while keeping finite-sample uncertainty explicit.

   • The Qubit: 5 lessons
   • Superposition: 5 lessons
   • Measurement & the Born Rule: 5 lessons
   • Phase & Observables: 5 lessons
   • Capstone: A Quantum Coin: 5 lessons

2. Quantum Gates & Circuits

   Build ideal unitary Pauli and Hadamard gates, compose chronological circuits and extend them with ordered tensor products and CNOT. Finish with a reusable circuit report that retains the full operators, states and probabilities.

   • Single-Qubit Gates: 5 lessons
   • The Hadamard Gate: 5 lessons
   • Quantum Circuits: 5 lessons
   • Multi-Qubit Systems: 5 lessons
   • The CNOT Gate: 5 lessons

3. Entanglement & Quantum Algorithms

   Study pure-state entanglement, conditional measurements and all branches of quantum teleportation, then assemble Grover amplitude amplification. The speedup is in the ideal oracle-query model; a classical state-vector simulation does not gain that speedup.

   • Entanglement: 5 lessons
   • Measuring Entangled Qubits: 5 lessons
   • Quantum Teleportation: 5 lessons
   • Grover's Search: 5 lessons
   • Capstone: Run a Quantum Algorithm: 5 lessons

4. Wavefunctions & the Schrodinger Equation

   Discretize one-dimensional wavefunctions and zero-Dirichlet Hamiltonians, solve their complete spectra and compare discrete box energies with continuum anchors. Explore the leading barrier attenuation model, then compose a box report with normalized states, density, region probability and discretization error.

   • Wavefunctions: 5 lessons
   • The Hamiltonian: 5 lessons
   • Energy Levels: 5 lessons
   • Quantum Tunneling: 5 lessons
   • Capstone: Solve a Quantum Well: 5 lessons

5. Randomness & Monte Carlo

   Simulate random walks, estimate areas and integrals by sampling, and relate statistical error to sample count under explicit assumptions. Assemble a reproducible diffusion experiment with full paths, time-dependent moments and physical step-length and time units.

   • Random Walks: 5 lessons
   • Estimating Pi: 5 lessons
   • Monte Carlo Integration: 5 lessons
   • The Law of Large Numbers: 5 lessons
   • Capstone: Simulate Diffusion: 5 lessons

6. Statistical Mechanics: The Ising Model

   Build periodic ferromagnetic Ising energy and local-flip models, then implement Metropolis sweeps and a temperature study. Retain burn-in, measurement traces and batch diagnostics, and separate a finite-lattice threshold estimate from the known infinite-lattice critical temperature.

   • Spins & Energy: 5 lessons
   • The Metropolis Algorithm: 5 lessons
   • Temperature & Equilibrium: 5 lessons
   • The Phase Transition: 5 lessons
   • Capstone: Find the Phase Transition: 5 lessons

7. Nonlinear Dynamics & Chaos

   Iterate the logistic map, inspect fixed points and recurrence, and estimate finite-time Lyapunov growth and sensitivity horizons. Explore explicit-Euler Lorenz trajectories and compose a dynamics report that can leave conclusions unresolved when the observation window is insufficient.

   • The Logistic Map: 5 lessons
   • The Route to Chaos: 5 lessons
   • The Butterfly Effect: 5 lessons
   • The Lorenz Attractor: 5 lessons
   • Capstone: Characterize Chaos: 5 lessons

8. Cellular Automata & Emergence

   Implement elementary binary rules and synchronous Conway Life updates with explicit boundaries. Retain complete histories to distinguish still patterns, oscillators and demonstrated glider translations; finite patterns and symmetry alone do not establish chaos or a universal classification.

   • Elementary Cellular Automata: 5 lessons
   • Chaos and Fractals: 5 lessons
   • Conway's Game of Life: 5 lessons
   • The Patterns of Life: 5 lessons
   • Capstone: Characterize Emergence: 5 lessons

9. Complex Networks

   Represent simple undirected graphs and measure degrees, clustering, components and shortest paths. Study a specified shortcut and deterministic synchronous SIR process, then compose a network report that preserves unreachable distances and finite-model limits.

   • Graphs and Networks: 5 lessons
   • Network Structure: 5 lessons
   • Paths and Small Worlds: 5 lessons
   • Spreading on Networks: 5 lessons
   • Capstone: Characterize a Network: 5 lessons

10. Capstone: Critical Phenomena

    Assemble an open-grid percolation study with retained trial fields and masks, cluster measurements, spanning probabilities, Wilson intervals and a nullable sampled crossing. Build driven sandpile experiments and synthetic power-law fits in separate chapters, distinguishing these finite observations from critical-exponent or universality evidence.

    • Percolation: 5 lessons
    • The Critical Threshold: 5 lessons
    • Self-Organized Criticality: 5 lessons
    • Power Laws and Universality: 5 lessons
    • Capstone: Characterize a Critical Transition: 5 lessons