# Quantum Physics API > Quantum and atomic-physics maths as an API, computed locally and deterministically. The photoelectric endpoint applies Einstein's photoelectric equation, KE = hf − φ — from the incident light's wavelength or frequency and a metal's work function it gives the photon energy, whether electrons are emitted, their maximum kinetic energy, the threshold frequency and wavelength (f₀ = φ/h), the maximum electron speed and the stopping voltage. The bohr endpoint computes the Bohr-model energy level Eₙ = −13.606·Z²/n² eV and orbital radius rₙ = 0.529·n²/Z Å of a hydrogen-like atom, the ionisation energy, and — given a second level — the wavelength of the emitted or absorbed photon. The rydberg endpoint computes a spectral line's wavelength from the Rydberg formula, 1/λ = R·Z²·(1/n₁² − 1/n₂²), and names its series (Lyman, Balmer, Paschen …) and spectral region. Everything is computed locally and deterministically, so it is instant and private. Ideal for physics-education, spectroscopy, astronomy and science app developers, atomic-physics and spectral tools, and STEM teaching. Pure local computation — no key, no third-party service, instant. Live, nothing stored. 3 endpoints. This is quantum and atomic physics; for electromagnetic wavelength and photon energy use a wavelength API and for special relativity a relativity API. ## Authentication All requests require your oanor API key in the `x-oanor-key` header. Get one at https://www.oanor.com/developer/keys. ```bash curl -H "x-oanor-key: oanor_live_…" "https://api.oanor.com/quantum-api/..." ``` ## Pricing - **Free** (Free) — 2,000 calls/Mo, 2 req/s - **Starter** ($5/Mo) — 25,000 calls/Mo, 5 req/s - **Pro** ($15/Mo) — 150,000 calls/Mo, 15 req/s - **Mega** ($45/Mo) — 638,000 calls/Mo, 40 req/s ## Endpoints ### Quantum #### `GET /v1/bohr` — Bohr model **Parameters:** - `level` (query, required, string) — Principal quantum number n Example: `2` - `atomic_number` (query, optional, string) — Atomic number Z Example: `1` - `to_level` (query, optional, string) — Second level for a transition **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/quantum-api/v1/bohr?level=2&atomic_number=1" ``` **Response:** ```json { "data": { "note": "Bohr model: Eₙ = −13.606·Z²/n² eV, rₙ = 0.529·n²/Z Å. n = 1 is the ground state.", "inputs": { "level": 2, "atomic_number": 1 }, "energy_j": -5.449680900000001e-19, "energy_ev": -3.401423, "orbital_radius_nm": 0.2116708, "ionization_energy_ev": 3.401423, "orbital_radius_angstrom": 2.116708 }, "meta": { "timestamp": "2026-06-05T03:08:58.775Z", "request_id": "7cc88c4c-5a54-4382-b5c3-ee0720b2d7f8" }, "status": "ok", "message": "Bohr model", "success": true } ``` #### `GET /v1/photoelectric` — Photoelectric effect **Parameters:** - `work_function` (query, required, string) — Work function φ (eV) Example: `2` - `wavelength` (query, optional, string) — Incident wavelength (nm) Example: `400` - `frequency` (query, optional, string) — Or frequency (Hz) **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/quantum-api/v1/photoelectric?work_function=2&wavelength=400" ``` **Response:** ```json { "data": { "note": "Photoelectric effect: KE = hf − φ. No electrons are emitted below the threshold frequency f₀ = φ/h.", "inputs": { "frequency_hz": 749481140000000, "work_function_ev": 2 }, "photon_energy_j": 4.966114600000001e-19, "photon_energy_ev": 3.099605, "electrons_emitted": true, "stopping_voltage_v": 1.099605, "max_electron_speed_ms": 621933.63, "max_kinetic_energy_ev": 1.099605, "threshold_frequency_hz": 483597850000000, "threshold_wavelength_nm": 619.921 }, "meta": { "timestamp": "2026-06-05T03:08:58.851Z", "request_id": "6ceb9a1b-33b8-4182-976e-00a94296a236" }, "status": "ok", "message": "Photoelectric", "success": true } ``` #### `GET /v1/rydberg` — Rydberg spectral line **Parameters:** - `n1` (query, required, string) — Lower level n₁ Example: `2` - `n2` (query, required, string) — Upper level n₂ Example: `3` - `atomic_number` (query, optional, string) — Atomic number Z Example: `1` **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/quantum-api/v1/rydberg?n1=2&n2=3&atomic_number=1" ``` **Response:** ```json { "data": { "note": "Rydberg formula: 1/λ = R·Z²·(1/n₁² − 1/n₂²), R = 1.0974×10⁷ m⁻¹. n₁ = 2 gives the visible Balmer series for hydrogen.", "inputs": { "n1": 2, "n2": 3, "atomic_number": 1 }, "region": "visible", "series": "Balmer", "wavenumber_m": 1524129.4, "wavelength_nm": 656.1123, "photon_energy_ev": 1.88968 }, "meta": { "timestamp": "2026-06-05T03:08:58.933Z", "request_id": "4f0cad5c-d267-45b1-a594-ab77020f8c6c" }, "status": "ok", "message": "Rydberg lines", "success": true } ``` ### Meta #### `GET /v1/meta` — Spec **Example:** ```bash curl -H "x-oanor-key: $KEY" \ "https://api.oanor.com/quantum-api/v1/meta" ``` **Response:** ```json { "data": { "notes": "Wavelengths in nm, frequency in Hz, energies in eV, work function in eV. Bohr/Rydberg take integer levels; Z is the atomic number (1 for hydrogen).", "service": "quantum-api", "formulae": { "rydberg": "1/λ = R·Z²·(1/n₁² − 1/n₂²)", "bohr_energy": "Eₙ = −13.606·Z²/n² eV", "photoelectric": "KE = hf − φ" }, "endpoints": { "GET /v1/bohr": "Bohr energy levels, orbital radius and transition wavelengths (hydrogen-like).", "GET /v1/meta": "This document.", "GET /v1/rydberg": "Spectral-line wavelength from the Rydberg formula and its series.", "GET /v1/photoelectric": "Max kinetic energy, threshold and electron speed from light and a work function." }, "description": "Quantum and atomic-physics calculator: the photoelectric effect, Bohr-model energy levels and orbital radii, and Rydberg spectral-line wavelengths." }, "meta": { "timestamp": "2026-06-05T03:08:59.006Z", "request_id": "a8287cc9-20ff-4d34-9e9f-09869673faef" }, "status": "ok", "message": "Meta", "success": true } ``` --- Marketplace page: https://www.oanor.com/api/quantum-api OpenAPI spec: https://www.oanor.com/api/quantum-api/openapi.json