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Wave Mechanics operators

24 operators in the wave_mechanics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
RHY1Zeq fundamental rhythm operator: sine wave at the 1.287 Hz HulyaPulse frequency.R_search = min |f_actual - 1.287| · φ(t)
RHY2Zeq harmonic series operator: superposition of N harmonics of the 1.287 Hz fundamental.H_integrity = ∫ |φ(t) - φ_pure|² dt
RHY3Damped-rhythm coupling: a sum of exponentially-decaying modes κ·e^(−|Δt|) in phase with the 1.287 Hz HulyaPulse.F_bond = Σ_k κ_k · e^(-|Δt|) · cos(2π·1.287·Δt)
RHY4Zeq amplitude-modulated rhythm: 1.287 Hz carrier modulated by a secondary frequency.φ_c^42 · ∑_{k=124,125} ZRO_k(Ψ) · sin(2π·1.287·t) · 0.85 · (Φ ∆ → Λ_eff ϕ(t) → Ψ(t))
WM1General traveling wave: sinusoidal displacement as a function of position, time, and phase.y = A\sin(kx - \omega t + \phi)
WM10Phase difference from path length difference for wave interference analysis.\Delta\phi = k\Delta x = \frac{2\pi}{\lambda}\Delta x
WM11Two-source interference pattern with constructive and destructive interference terms.I = I_1 + I_2 + 2\sqrt{I_1 I_2}\cos\Delta\phi
WM12Diffraction angle for single-slit diffraction: wavelength divided by slit width.\theta_d = \frac{\lambda}{d}
WM13Diffraction grating constructive interference condition for multiple slits.d\sin\theta = n\lambda
WM14Single-slit diffraction minima condition for destructive interference.a\sin\theta = m\lambda
WM15Critical angle for total internal reflection when light passes from denser to rarer medium.\sin\theta_c = \frac{n_2}{n_1}
WM16Time-independent Schrödinger equation in one dimension for energy eigenvalue problems.\frac{\partial^2 \psi}{\partial x^2} + \frac{2m}{\hbar^2}(E-V)\psi = 0
WM17De Broglie wavelength relating a particle's wavelength to its momentum.\lambda = \frac{h}{p}
WM18Heisenberg uncertainty principle for position and momentum.\Delta x \Delta p \geq \frac{\hbar}{2}
WM19Plane wave solution: complex exponential representing a free particle with definite momentum.\psi(x,t) = Ae^{i(kx - \omega t)}
WM2Phase velocity of a wave: ratio of angular frequency to wave number, or frequency times wavelength.v = \frac{\omega}{k} = f\lambda
WM20Planck-Einstein and de Broglie relations connecting energy to frequency and momentum to wave number.E = \hbar\omega, \quad p = \hbar k
WM3Classical wave equation: second time derivative of displacement equals wave speed squared times spatial Laplacian.\frac{\partial^2 y}{\partial t^2} = v^2\frac{\partial^2 y}{\partial x^2}
WM4Standing wave formed by superposition of two counter-propagating waves.y = 2A\cos(kx)\sin(\omega t)
WM5Wave number and angular frequency definitions relating to wavelength and frequency.k = \frac{2\pi}{\lambda}, \quad \omega = 2\pi f
WM6Group velocity: the velocity at which a wave packet's envelope propagates, d(omega)/dk.v_g = \frac{d\omega}{dk}
WM7Phase velocity: the speed at which a single frequency component of a wave travels.v_p = \frac{\omega}{k}
WM8Wave intensity proportional to the square of the amplitude.I \propto A^2
WM9Superposition of two waves producing interference with amplitude modulation.y_{total} = y_1 + y_2 = 2A\cos(\Delta\phi/2)\sin(kx - \omega t + \bar{\phi})

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["RHY1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​