Contract
- Input: problem description and inputs defined by the skill body.
- Output: Markdown artifact with completed process steps.
- Side effects: none.
- Dependencies: none.
- Stop condition: all process steps executed; artifact saved with required sections.
- Risk: low.
- Boundary: produces reasoning artifact only; no system changes.
Quantum Physics Modeling
Construct a quantum model of a system — state space, Hamiltonian, measurement — and answer a question about it with explicit regime checks.
When to use
- The user wants to model a quantum system or compute an observable.
- A claim from quantum information, quantum computing, atomic/molecular physics, or condensed matter needs grounding.
- Another skill (e.g.
cs-cryptography or quantum-related ML) needs a quantum-mechanical sub-model.
Process
1. Define the system
Specify:
- Hilbert space — finite (qubits, spin-1/2) or infinite (position, Fock).
- Basis — computational, Fock, position, momentum.
- State — pure |ψ⟩ or mixed ρ; for multi-party, identify subsystems.
- Hamiltonian — kinetic + potential; cite which interactions are kept.
Completion criterion: Hilbert space, basis, state, and Hamiltonian all explicit.
2. Identify the regime
Locate the system in the taxonomy:
- Non-relativistic vs relativistic (Schrödinger vs Dirac).
- Single-particle vs many-body.
- Closed vs open (Lindblad master equation if open).
- Discrete (qubit) vs continuous-variable.
Pick the right formalism: Schrödinger picture, Heisenberg, interaction picture, path integral.
Completion criterion: regime and formalism chosen with a one-line justification.
3. Compute
Solve by the path that matches the system:
- Exactly solvable — harmonic oscillator, hydrogen, two-level, Jaynes–Cummings.
- Perturbation theory — time-independent or time-dependent; cite the small parameter.
- Variational — ansatz + minimize ⟨ψ|H|ψ⟩.
- Numerical — exact diagonalisation, DMRG, tensor networks, QMC.
For each step, state approximations and truncations.
Completion criterion: method named, approximations listed, computation executed.
4. Units and limits check
- Units: verify ℏ, c, k_B are set correctly; energies, lengths, times have plausible orders of magnitude.
- Limits: check classical limit (ℏ→0), continuum limit, weak-coupling limit, large-N limit.
- Symmetries: confirm the answer respects them (rotational, particle-number, parity).
Completion criterion: units sanity-checked; at least one limit recovered.
5. Deliver
Markdown artifact with: system definition, regime, computation, units/limits, and the answer with an uncertainty or approximation note. Cite the method used.
Completion criterion: artifact covers all five; answer is reproducible.
1---2name: physics-quantum3description: Model quantum systems (states, operators, measurement, entanglement) and perform calculations using Dirac notation, with checks against limits and known results.4---56## Contract78- **Input:** problem description and inputs defined by the skill body.9- **Output:** Markdown artifact with completed process steps.10- **Side effects:** none.11- **Dependencies:** none.12- **Stop condition:** all process steps executed; artifact saved with required sections.13- **Risk:** low.14- **Boundary:** produces reasoning artifact only; no system changes.151617# Quantum Physics Modeling1819Construct a **quantum model** of a system — state space, Hamiltonian, measurement — and answer a question about it with explicit regime checks.2021## When to use2223- The user wants to model a quantum system or compute an observable.24- A claim from quantum information, quantum computing, atomic/molecular physics, or condensed matter needs grounding.25- Another skill (e.g. `cs-cryptography` or quantum-related ML) needs a quantum-mechanical sub-model.2627## Process2829### 1. Define the system3031Specify:3233- **Hilbert space** — finite (qubits, spin-1/2) or infinite (position, Fock).34- **Basis** — computational, Fock, position, momentum.35- **State** — pure |ψ⟩ or mixed ρ; for multi-party, identify subsystems.36- **Hamiltonian** — kinetic + potential; cite which interactions are kept.3738**Completion criterion:** Hilbert space, basis, state, and Hamiltonian all explicit.3940### 2. Identify the regime4142Locate the system in the taxonomy:4344- Non-relativistic vs relativistic (Schrödinger vs Dirac).45- Single-particle vs many-body.46- Closed vs open (Lindblad master equation if open).47- Discrete (qubit) vs continuous-variable.4849Pick the right formalism: Schrödinger picture, Heisenberg, interaction picture, path integral.5051**Completion criterion:** regime and formalism chosen with a one-line justification.5253### 3. Compute5455Solve by the path that matches the system:5657- **Exactly solvable** — harmonic oscillator, hydrogen, two-level, Jaynes–Cummings.58- **Perturbation theory** — time-independent or time-dependent; cite the small parameter.59- **Variational** — ansatz + minimize ⟨ψ|H|ψ⟩.60- **Numerical** — exact diagonalisation, DMRG, tensor networks, QMC.6162For each step, state approximations and truncations.6364**Completion criterion:** method named, approximations listed, computation executed.6566### 4. Units and limits check6768- **Units:** verify ℏ, c, k_B are set correctly; energies, lengths, times have plausible orders of magnitude.69- **Limits:** check classical limit (ℏ→0), continuum limit, weak-coupling limit, large-N limit.70- **Symmetries:** confirm the answer respects them (rotational, particle-number, parity).7172**Completion criterion:** units sanity-checked; at least one limit recovered.7374### 5. Deliver7576Markdown artifact with: system definition, regime, computation, units/limits, and the answer with an uncertainty or approximation note. Cite the method used.7778**Completion criterion:** artifact covers all five; answer is reproducible.
quantumquirkxyz