L1 ⚛ L1-313 ⊙ Testnet

Time-Dependent Schrödinger Equation

Quantum Mechanics · Quantum dynamics

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⬇ L1-313.md

# ⚛ L1 Principle — Time-Dependent Schrödinger Equation **ID:** `L1-313` · **Status:** ⊙ Testnet (genesis catalog) > **🌐 Domain:** Quantum Mechanics — *Quantum dynamics* > **🎯 Problem class:** nonlinear inverse · **🧮 Solution space:** time dependent wavefunction > **📡 Carrier:** electron · **🌫 Noise:** gaussian > **⚖ Difficulty (δ):** 5 · **⛓ Block:** 41554079 --- ## 🧠 1. Introduction **Time-Dependent Schrödinger Equation** is a **nonlinear inverse problem** whose unknown lives in **time dependent wavefunction** space, within the **Quantum dynamics** sub-domain of **Quantum Mechanics**. Measurements consist of electrons collected by an electron detector via a **pump probe spectroscopy** sensing mechanism. The forward operator applies, in order: E · hamiltonian t operator; E · laser coupling operator; time evolution of the state; O · time resolved operator. Observations are corrupted by additive Gaussian noise. Unitary evolution bounded; inversion ill-conditioned due to phase ambiguity. ## ⚙ 2. Forward Model Physical chain: **x** → E · hamiltonian t → E · laser coupling → Time derivative → O · time resolved → **y** (detector). ``` y = `O.time_resolved` ∂_t `E.laser_coupling` `E.hamiltonian_t` x + n, n ~ 𝒩(0, σ²) ``` **Measurement DAG:** | Primitive | What it does | |---|---| | `E.hamiltonian_t` | E · hamiltonian t operator | | `E.laser_coupling` | E · laser coupling operator | | `D.time` | Time evolution of the state | | `O.time_resolved` | O · time resolved operator | ## 🔬 3. Physics Fingerprint | Property | Value | |---|---| | Domain | Quantum Mechanics | | Sub domain | Quantum dynamics | | Carrier | electron | | Problem class | nonlinear_inverse | | Solution space | time_dependent_wavefunction | | Noise model | gaussian | | Integration axis | time | | Difficulty delta | 5 | | L dag | 3.5 | ## 📡 4. Measurement Model Unitary evolution bounded; inversion ill-conditioned due to phase ambiguity. | Metric | Value | |---|---| | Metric | transition_probability_error | | Secondary | HHG_spectrum_L2 | ## 📏 5. Operating Range (Ω) **Center problem class:** `time_dependent_schrodinger` · **Forward operator:** `TDSE_forward` **Center point:** | Parameter | Unit | Value | |---|---|---| | N grid | — | 2048 | | T end fs | — | 100 | | Lambda nm | nm | 800 | | N electrons | — | 1 | | I laser w cm2 | — | 1e+13 | **Allowed bounds:** | Parameter | Unit | Range | |---|---|---| | N grid | — | 256 – 1048576 | | T end fs | — | 0.1 – 1000000.0 | | Lambda nm | nm | 50 – 10000 | | N electrons | — | 1 – 1000 | | I laser w cm2 | — | 10000000000.0 – 100000000000000000000 | ## 🎯 6. Tolerance (ε) **Center tolerance:** P_trans error <= 0.015 | Metric | Range | |---|---| | Transition probability error | 0.001 – 0.5 | ## ⚖ 7. Hardness Function Hardness scales as **`epsilon_fn`** on **transition_probability_error**, with κ = `700` and δ = `5`. ## 💾 8. Reference Dataset - **primary** · weight 1.0 · IPFS _(not pinned yet)_ ## 9. On-chain Registration - **Chain hash:** `0x69522f25a3b893dd98218670cf5fdbb66e28c240c837a01e4e2ac12a83c6a6ac` - **Chain tx hash:** `0x7450a1b24a87c9d7aa012ae13f90653523893fa18b6eda0c1265981191e8b17f` - **Chain block:** `41554079` --- ## File Mapping This bundle consists of: `L1-313.md`, `L1-313.json`. | File | Role | How to regenerate | |------|------|-------------------| | `L1-313.md` | Source of truth — edit this | Human or LLM | | `L1-313.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 `L1-313`._ _Edit it, regenerate the JSON, and submit at [/submit](/submit) to claim the artifact._

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Read the attached Markdown (L1-313.md).
Regenerate L1-313.json so every field matches the Markdown.
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Output each file in its own fenced code block tagged with the filename.

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L2-313-001 Time-Dependent Schrödinger Equation Mismatch-Only Spec

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📋 JSON metadata

{
  "artifact_id": "L1-313",
  "chain_block": 41554079,
  "chain_hash": "0x69522f25a3b893dd98218670cf5fdbb66e28c240c837a01e4e2ac12a83c6a6ac",
  "chain_tx_hash": "0x7450a1b24a87c9d7aa012ae13f90653523893fa18b6eda0c1265981191e8b17f",
  "domain": "Quantum Mechanics",
  "hardness_fn": {
    "delta": 5,
    "kappa": 700,
    "metric": "transition_probability_error",
    "type": "epsilon_fn"
  },
  "initiator_dataset": [
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      "ipfs_cid": null,
      "license_hash": null,
      "name": "primary",
      "weight": 1.0
    }
  ],
  "layer": "L1",
  "observable_profile": {
    "metric": "transition_probability_error",
    "regime": "Unitary evolution bounded; inversion ill-conditioned due to phase ambiguity.",
    "secondary": "HHG_spectrum_L2"
  },
  "physics_fingerprint": {
    "L_DAG": 3.5,
    "carrier": "electron",
    "difficulty_delta": 5,
    "domain": "Quantum Mechanics",
    "integration_axis": "time",
    "noise_model": "gaussian",
    "primitives": [
      "E.hamiltonian_t",
      "E.laser_coupling",
      "D.time",
      "O.time_resolved"
    ],
    "problem_class": "nonlinear_inverse",
    "sensing_mechanism": "pump_probe_spectroscopy",
    "solution_space": "time_dependent_wavefunction",
    "sub_domain": "Quantum dynamics",
    "title": "Time-Dependent Schr\u00f6dinger Equation"
  },
  "size_tiers": {
    "allowed_forward_operators": [
      "TDSE_forward"
    ],
    "allowed_omega_dimensions": [
      "N_grid",
      "T_end_fs",
      "I_laser_W_cm2",
      "lambda_nm",
      "N_electrons"
    ],
    "allowed_problem_classes": [
      "time_dependent_schrodinger"
    ],
    "center_spec": {
      "epsilon_fn_center": "P_trans error \u003c= 0.015",
      "forward_operator": "TDSE_forward",
      "input_format": "measurement_only",
      "omega": {
        "I_laser_W_cm2": 10000000000000.0,
        "N_electrons": 1,
        "N_grid": 2048,
        "T_end_fs": 100,
        "lambda_nm": 800
      },
      "problem_class": "time_dependent_schrodinger"
    },
    "epsilon_bounds": {
      "transition_probability_error": [
        0.001,
        0.5
      ]
    },
    "omega_bounds": {
      "I_laser_W_cm2": [
        10000000000.0,
        100000000000000000000
      ],
      "N_electrons": [
        1,
        1000
      ],
      "N_grid": [
        256,
        1048576
      ],
      "T_end_fs": [
        0.1,
        1000000.0
      ],
      "lambda_nm": [
        50,
        10000
      ]
    }
  },
  "staked_pwm": 0.0,
  "status": "testnet",
  "sub_domain": "Quantum dynamics",
  "title": "Time-Dependent Schr\u00f6dinger Equation"
}

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