L1 ⚛ L1-312 ⊙ Testnet

Time-Independent Schrödinger Equation

Quantum Mechanics · Stationary quantum eigenproblem

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⬇ L1-312.md

# ⚛ L1 Principle — Time-Independent Schrödinger Equation **ID:** `L1-312` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Stationary quantum eigenproblem* > **🎯 Problem class:** linear inverse · **🧮 Solution space:** wavefunctions and eigenvalues > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554079 --- ## 🧠 1. Introduction **Time-Independent Schrödinger Equation** is a **linear inverse problem** whose unknown lives in **wavefunctions and eigenvalues** space, within the **Stationary quantum eigenproblem** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **spectroscopic transition** sensing mechanism. The forward operator applies, in order: E · hamiltonian operator; computes eigen-pairs of a linear operator; O · spectra wavefunctions operator. Observations are corrupted by additive Gaussian noise. Eigenvalues real under self-adjointness; inversion of V(r) from spectrum is the inverse Sturm-Liouville problem (ill-posed for incomplete data). ## ⚙ 2. Forward Model Physical chain: **x** → E · hamiltonian → O · spectra wavefunctions → **y** (detector). ``` y = `O.spectra_wavefunctions` `E.hamiltonian` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.hamiltonian` | E · hamiltonian operator | | `O.spectra_wavefunctions` | O · spectra wavefunctions operator | **🛠 Solver components** _(used inside the solver, not in the forward equation)_: | Primitive | What it does | |---|---| | `E.eigensolve` | Computes eigen-pairs of a linear operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Stationary quantum eigenproblem | | Carrier | electron | | Problem class | linear_inverse | | Solution space | wavefunctions_and_eigenvalues | | Noise model | gaussian | | Integration axis | energy | | Difficulty delta | 5 | | L dag | 3 | ## 📡 4. Measurement Model Eigenvalues real under self-adjointness; inversion of V(r) from spectrum is the inverse Sturm-Liouville problem (ill-posed for incomplete data). | Metric | Value | |---|---| | Metric | energy_error_eV | | Secondary | wavefunction_L2_error | ## 📏 5. Operating Range (Ω) **Center problem class:** `time_independent_schrodinger` · **Forward operator:** `schrodinger_stationary_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N basis | — | 1000 | | N eigen | — | 20 | | Box size a | — | 10 | | Potential type | — | harmonic | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N basis | — | 100 – 100000 | | N eigen | — | 1 – 1000 | | Box size a | — | 1 – 1000 | | Potential type | — | harmonic, coulomb, square_well, double_well | ## 🎯 6. Tolerance (ε) **Center tolerance:** E_n error <= 0.01 eV | Metric | Range | |---|---| | Energy error ev | 0.001 – 1.0 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **energy_error_eV**, with κ = `500` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0xab0f3547902121b91cd7d7ed4ca2213f07a0e1a6b61e44b79c9739ff9fe2b819` - **Chain tx hash:** `0x573f7d6dbd01c915c0c21a66d22fb71fc0c3ff3d1a0a01ac884d144356ec230c` - **Chain block:** `41554079` --- ## File Mapping This bundle consists of: `L1-312.md`, `L1-312.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-312.md` | Source of truth — edit this | Human or LLM | | `L1-312.json` | Structured metadata for the registry | LLM regenerates from the sections above | **Prompt for your LLM after editing this Markdown:** > Read the attached Markdown. Regenerate the sibling `.json` so every field matches. > Preserve the schema documented in the rows above. > Output each file in its own fenced code block tagged with the filename. > Output only the JSON object. _This Markdown was auto-synthesized from the catalog row for `L1-312`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-312.md).
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L2-312-001 Time-Independent Schrödinger Equation Mismatch-Only Spec

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📋 JSON metadata

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  "chain_block": 41554079,
  "chain_hash": "0xab0f3547902121b91cd7d7ed4ca2213f07a0e1a6b61e44b79c9739ff9fe2b819",
  "chain_tx_hash": "0x573f7d6dbd01c915c0c21a66d22fb71fc0c3ff3d1a0a01ac884d144356ec230c",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
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    "regime": "Eigenvalues real under self-adjointness; inversion of V(r) from spectrum is the inverse Sturm-Liouville problem (ill-posed for incomplete data).",
    "secondary": "wavefunction_L2_error"
  },
  "physics_fingerprint": {
    "L_DAG": 3.0,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Quantum Mechanics",
    "integration_axis": "energy",
    "noise_model": "gaussian",
    "primitives": [
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      "E.eigensolve",
      "O.spectra_wavefunctions"
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    "problem_class": "linear_inverse",
    "sensing_mechanism": "spectroscopic_transition",
    "solution_space": "wavefunctions_and_eigenvalues",
    "sub_domain": "Stationary quantum eigenproblem",
    "title": "Time-Independent Schr\u00f6dinger Equation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "schrodinger_stationary_forward"
    ],
    "allowed_omega_dimensions": [
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      "N_eigen",
      "box_size_A",
      "potential_type"
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    "allowed_problem_classes": [
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    "center_spec": {
      "epsilon_fn_center": "E_n error \u003c= 0.01 eV",
      "forward_operator": "schrodinger_stationary_forward",
      "input_format": "measurement_only",
      "omega": {
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        "N_eigen": 20,
        "box_size_A": 10,
        "potential_type": "harmonic"
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    "epsilon_bounds": {
      "energy_error_eV": [
        0.001,
        1.0
      ]
    },
    "omega_bounds": {
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        100000
      ],
      "N_eigen": [
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      ],
      "box_size_A": [
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        1000
      ],
      "potential_type": [
        "harmonic",
        "coulomb",
        "square_well",
        "double_well"
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Stationary quantum eigenproblem",
  "title": "Time-Independent Schr\u00f6dinger Equation"
}

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