Psi in LaTeX (\psi)

Where it is used

Lowercase Greek psi, the conventional letter for a quantum wavefunction and the digamma function.

Quantum mechanics writes wavefunctions as \psi(x, t) and states as |\psi\rangle in Dirac notation, with the Schrödinger equation i\hbar\,\partial_t \psi = \hat{H}\psi. Special functions use \psi(x) = \Gamma'(x)/\Gamma(x) for the digamma function. Fluid dynamics uses \psi for the stream function, and wavelet analysis uses \psi for a mother wavelet. For bra-ket notation, \langle \psi | \phi \rangle uses \langle and \rangle, not less-than and greater-than signs. The uppercase \Psi is a separate command. Normalization requires \int |\psi|^2\,dx = 1.

Minimal compilable example

Paste this into an empty .tex file and compile it with pdfLaTeX, XeLaTeX or LuaLaTeX.

\documentclass{article}
\begin{document}
Psi: $\psi$

\[ i\hbar \frac{\partial}{\partial t} \psi(x, t) = \hat{H} \psi(x, t) \]
\end{document}

Related symbols

• Psi (Upper)\Psi
• Chi\chi
• Omega\omega
• Phi (Upper)\Phi
• Omega (Upper)\Omega
• Phi\phi

Frequently asked questions

How do I write Psi in LaTeX?

Type \psi in math mode, for example $i\hbar \frac{\partial}{\partial t} \psi(x, t) = \hat{H} \psi(x, t)$. It works in plain LaTeX without loading any package.

Which package do I need for \psi?

None. \psi is part of standard LaTeX, so it compiles with nothing in the preamble but the document class.

Can I use \psi in text mode, or only in math mode?

Only in math mode. Outside $...$ LaTeX stops with "Missing $ inserted", so write $\psi$ in running text. If you only need the glyph in text, paste the Unicode character ψ instead (with XeLaTeX or LuaLaTeX and a font that has it).