TeXipedia

psi

Represents a versatile Greek letter commonly used in physics, mathematics, and statistics as a variable or function symbol.

Overview

Widely employed across scientific disciplines, particularly in quantum mechanics where it denotes wave functions and state vectors. Also appears frequently in:

  • Statistical analysis for probability functions
  • Mathematical physics for potential functions
  • Psychology and social sciences as a statistical symbol
  • Chemistry for molecular orbitals and electron configurations

Both uppercase and lowercase variants carry distinct conventional meanings depending on the field of study, making it one of the more flexible Greek letters in scientific notation.

Examples

Wave function in quantum mechanics.

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

Eigenfunction expansion in mathematical physics.

f(x)=∑n=1∞cnψn(x)f(x) = \sum_{n=1}^{\infty} c_n \psi_n(x) 
f(x) = \sum_{n=1}^{\infty} c_n \psi_n(x)

Statistical mechanics partition function.

Z=∑ne−En/kT⟨ψn∣ψn⟩Z = \sum_n e^{-E_n/kT} \langle \psi_n | \psi_n \rangle 
Z = \sum_n e^{-E_n/kT} \langle \psi_n | \psi_n \rangle