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Quantum & Atomic Physics

Heisenberg Uncertainty Principle

A fundamental quantum limit stating that canonical conjugate physical variables (such as position and momentum, or energy and time) cannot…

Δx Δp ≥ ℏ / 2, ΔE Δt ≥ ℏ / 2 J·s (Action Units) Thermodynamics & Statistical Physics

Helmholtz Free Energy

A thermodynamic potential measuring maximum reversible work obtainable from a closed system at constant temperature and volume.

F = U - T S, dF = -S dT - P dV J Biophysics & Medical Physics

Hemodynamics

The physical study of blood flow dynamics, vascular resistance, and pressure relations within the circulatory system.

Q = ΔP / R_v, R_v = (8 η L) / (π r⁴) (Poiseuille Flow) L/min (Cardiac Output) & mmHg (Pressure) Mathematical & Computational Physics

Hermite Polynomials

A sequence of classical orthogonal polynomials satisfying Hermite's differential equation y'' - 2x y' + 2n y = 0.

H_n(x) = (-1)^n e^(x²) (d^n / dx^n) (e^(-x²)) Dimensionless Orthogonal Polynomials Astrophysics, Cosmology & Relativity

Hertzsprung-Russell (H-R) Diagram

A foundational scatter plot of stellar luminosity versus surface temperature (or spectral type) used to trace stellar evolution phases.

L ∝ R² T^4 (Plot of Absolute Magnitude vs Spectral Type) Luminosity (L_☉) vs Surface Temp (K) Mathematical & Computational Physics

Hessian Matrix

A square matrix of second-order partial derivatives of a scalar-valued function, describing local surface curvature and local extrema…

H_ij = ∂²f / (∂x_i ∂x_j) Second Derivative Matrix Nuclear & Particle Physics

Higgs Boson

An elementary scalar boson associated with the Higgs field that endows fundamental particles with rest mass via electroweak symmetry…

m_H ≈ 125.1 GeV/c², Spin = 0, Scalar Field φ GeV/c² (Mass Energy) Mathematical & Computational Physics

Hilbert Space

A complete abstract vector space possessing an inner product that allows length and angle to be defined for infinite-dimensional function…

⟨f, g⟩ = ∫ f*(x) g(x) dx, ||f|| = √(⟨f, f⟩) Complete Inner Product Space Optics

Holography

A technique for recording and reconstructing 3D wavefields by recording phase and amplitude interference patterns between object and…

I(x,y) = |E_ref + E_obj|² N/A Classical Mechanics

Hooke's Law

A law of elasticity stating that restoring force exerted by a spring or elastic material is proportional to its extension or compression…

F = -k x N (k in N/m) Astrophysics, Cosmology & Relativity

Hubble's Law

The cosmological observation that galaxies recede from Earth at velocities directly proportional to their proper distance.

v = H₀ d, H₀ ≈ 70 (km/s) / Mpc km/s/Mpc (Hubble Constant) Quantum & Atomic Physics

Hund's Rule of Maximum Multiplicity

A rule stating that when filling degenerate atomic orbitals, electrons occupy separate orbitals singly with parallel spins before pairing…

S_total = ∑ s_i (Maximized spin in degenerate orbitals) Dimensionless Rule Waves, Oscillations & Acoustics

Huygens-Fresnel Principle

The wave propagation principle asserting that every point on a wavefront acts as a secondary source of spherical wavelets.

New Wavefront = Envelope of Secondary Wavelets N/A Quantum & Atomic Physics

Hydrogen Spectrum

The set of discrete electromagnetic emission and absorption lines produced when the electron in a hydrogen atom transitions between energy…

1 / λ = R_H (1 / n_f² - 1 / n_i²) m⁻¹ (Wavenumber) Geophysics & Environmental Physics

Hydrologic Cycle

The continuous global movement and transformation of water through Earth's atmosphere, land surface, oceans, and subsurface aquifers.

Water Balance: P = E + R + ΔS (Precipitation = Evaporation + Runoff + Storage Change) Global Water Flux (km³/year) Geophysics & Environmental Physics

Hydrothermal Vents

Fissures on the ocean floor near volcanically active mid-ocean ridges that vent geothermally heated, mineral-rich seawater into the ocean.

Geothermally Heated Seawater T ~ 350–400 °C °C (Vent Fluid Temperature) Quantum & Atomic Physics

Hyperfine Structure

Extremely small energy level splittings in atoms caused by interaction between nuclear magnetic moments and electron magnetic fields.

ΔE_HFS ∝ I_nucleus · J_electron eV or MHz (Small Energy Splitting) Foundations of Physics

Hypothesis

A proposed, testable explanation for an observed physical phenomenon, serving as the starting point for experimental investigation.

N/A Geophysics & Environmental Physics

Ice Core Analysis

The retrieval and paleoclimatological analysis of cylindrical ice samples extracted from deep polar ice sheets and alpine glaciers.

Paleotemperature Proxy δ¹⁸O = ((¹⁸O/¹⁶O)_sample / (¹⁸O/¹⁶O)_standard - 1) × 1000‰ Parts per thousand (‰ δ¹⁸O) / ppm (CO₂) Thermodynamics & Statistical Physics

Ideal Gas Law

The equation of state relating pressure, volume, temperature, and quantity of an ideal gas composed of non-interacting point particles.

P V = n R T = N kB T Pa·m³ = J Classical Mechanics

Impulse

The vector quantity defined as the integral of a force over the time interval during which it acts, equal to the net change in momentum.

J = ∫ F dt = Δp = m vf - m vi N·s (or kg·m/s) Classical Mechanics

Inclined Plane

A simple machine consisting of a flat supporting surface tilted at an angle to the horizontal.

MA = L / h = 1 / sin θ Dimensionless Foundations of Physics

Independent Variable

The experimental condition or factor intentionally manipulated by the researcher to observe its effect on an outcome.

Various Electromagnetism & Electronics

Inductive Reactance

The opposition offered by an inductor to alternating current flow, directly proportional to AC frequency and inductance.

X_L = 2π f L = ω L Ω (Ohms)