TeXipedia

varphi

Represents an alternative form of the Greek letter phi, commonly used in mathematics and physics to denote angles, phases, or scalar fields.

Overview

Provides a more cursive or flowing variant of the phi symbol, distinguished from the standard \phi by its distinctive curved shape. This version is particularly prevalent in:

  • Mathematical physics for representing wave functions and potential fields
  • Geometry and trigonometry for angle measurements
  • Statistical mechanics for partition functions
  • Quantum mechanics for state vectors

Many mathematicians and physicists prefer this variant for its aesthetic appeal and clearer distinction from similar symbols in handwritten work.

Examples

Using varphi as an angle in trigonometric expressions

sin⁡(φ)=32 when φ=π3\sin(\varphi) = \frac{\sqrt{3}}{2} \text{ when } \varphi = \frac{\pi}{3} 
\sin(\varphi) = \frac{\sqrt{3}}{2} \text{ when } \varphi = \frac{\pi}{3}

Representing phase in quantum mechanics

ψ(x,t)=Aei(kx−φ)\psi(x,t) = A e^{i(kx - \varphi)} 
\psi(x,t) = A e^{i(kx - \varphi)}

Golden ratio definition using varphi

φ=1+52≈1.618034\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.618034 
\varphi = \frac{1 + \sqrt{5}}{2} \approx 1.618034