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Optics

Paraxial Approximation

A small-angle approximation in geometric optics assuming light rays make small angles $θ$ with the optical axis.

sin θ ≈ θ, tan θ ≈ θ, cos θ ≈ 1 rad (radians) Nuclear & Particle Physics

Parity Violation

The discovery that the weak nuclear force distinguishes between left-handed and right-handed spatial orientations, violating spatial mirror…

P |Ψ(x, y, z)⟩ = - |Ψ(-x, -y, -z)⟩ (Violated in weak decays) Symmetry Violation Astrophysics, Cosmology & Relativity

Parsec

An astronomical unit of distance equal to the distance at which a star exhibits a trigonometric parallax angle of exactly one arcsecond…

1 pc = 1 AU / tan(1″) ≈ 3.2616 ly ≈ 3.0857 × 10¹⁶ m Parsecs (pc, kpc, Mpc) Mathematical & Computational Physics

Partial Differential Equations

Differential equations containing unknown multivariable functions and their partial derivatives with respect to multiple independent…

Elliptic (Laplace), Parabolic (Heat), Hyperbolic (Wave) Multivariable Differential Equations Quantum & Atomic Physics

Particle in a Box

A elementary quantum model describing a particle trapped inside a 1D rigid box with impenetrable potential barriers (infinite potential…

E_n = (n² π² ℏ²) / (2 m L²), ψ_n(x) = √(2/L) sin(n π x / L) eV or Joules Thermodynamics & Statistical Physics

Partition Function

The central mathematical function in statistical mechanics that encodes statistical properties of a system in thermodynamic equilibrium.

Z = ∑ exp(-E_i / (kB T)) = ∑ g_i exp(-E_i / (kB T)) Dimensionless Classical Mechanics

Pascal's Principle

The principle stating that pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and container…

ΔP = F1 / A1 = F2 / A2 Pa Quantum & Atomic Physics

Paschen Series

The spectral series of hydrogen atom emission lines produced by electron transitions dropping from upper energy states to the n=3 level.

1 / λ = R_H (1 / 3² - 1 / n_i²), n_i = 4, 5, 6... Infrared Wavelengths (nm) Biophysics & Medical Physics

Patch Clamp Technique

An electrophysiological laboratory technique used to record ion currents flowing through single individual ion channel proteins in cell…

I_single_channel ~ 1–10 pA (Gigaohm Seal Measurement) pA (Picoamperes) & GΩ (Gigaohm Resistance) Quantum & Atomic Physics

Pauli Exclusion Principle

A fundamental quantum law stating that two identical fermions cannot occupy the exact same quantum state simultaneously.

No two identical fermions can occupy the same quantum state: ψ(1,2) = -ψ(2,1) Dimensionless Quantum Law Condensed Matter & Materials Physics

Peltier Effect

The absorption or emission of heat at the junction of two dissimilar electrical conductors when an electric current flows across it.

Q_rate = Π_AB I = (S_A - S_B) T I W (Cooling / Heating Rate) Foundations of Physics

Percentage Uncertainty

The absolute uncertainty of a measurement divided by the measured value, expressed as a percentage.

Percentage Uncertainty = (Δx / x) × 100% % Classical Mechanics

Period

The time duration required to complete one full cycle of a recurring motion or oscillation.

T = 1 / f = 2π / ω = 2π √(m/k) s Classical Mechanics

Perpendicular Axis Theorem

A theorem stating that for a thin planar lamina, the moment of inertia about an axis perpendicular to the plane equals the sum of moments…

Iz = Ix + Iy kg·m² Mathematical & Computational Physics

Perturbation Theory

A set of mathematical approximation methods for finding an approximate solution to a complex problem by starting from the exact solution of…

H = H₀ + λ H', E_n = E_n^(0) + λ E_n^(1) + λ² E_n^(2) + ... Approximation Power Series Waves, Oscillations & Acoustics

Phase

The fractional position of a point within a wave cycle, expressed as an angle relative to a reference origin.

Φ(x,t) = k x - ω t + φ0 rad (radians) Waves, Oscillations & Acoustics

Phase Difference

The angular difference between corresponding points on two waves or between different points on a single wave.

Δφ = (2π / λ) Δx = (2π / T) Δt rad (radians) Waves, Oscillations & Acoustics

Phase Velocity

The speed at which a single monochromatic wave crest or phase front advances through a medium.

v_p = ω / k = f λ m/s Condensed Matter & Materials Physics

Phonon

A quantized collective vibrational wave excitation traveling through the periodic atomic or molecular lattice of a solid.

E = (n + ½) ℏ ω, p_crystal = ℏ q eV or J (Phonon Energy) Quantum & Atomic Physics

Phosphorescence

A type of photoluminescence where absorbed energy is emitted slowly over time due to spin-forbidden quantum transitions.

τ_phosphorescence ~ 10⁻³ s to hours Seconds to Hours (Lifetime) Quantum & Atomic Physics

Photoelectric Effect

The emission of electrons from a metal surface when light of frequency above a threshold value shines upon it.

K_max = h ν - Φ = e V_stopping eV or Joules Foundations of Physics

Physical Quantity

A quantifiable property of a physical system or phenomenon that can be measured and expressed as a numerical value multiplied by a unit.

Quantity = Value × Unit Various Mathematical & Computational Physics

Physical Simulation

The use of computer programs and numerical algorithms to simulate the time-dependent physical behavior of real-world or theoretical systems.

x(t + Δt) = x(t) + v(t) Δt + ½ a(t) Δt² Computational Modeling Condensed Matter & Materials Physics

Piezoelectric Effect

The generation of electric polarization charge in non-centrosymmetric crystals when subjected to mechanical stress (and vice versa).

Direct: P_i = d_ijk σ_jk; Reverse: ε_jk = d_ijk E_i C/N or m/V (Piezoelectric Coefficient d)