Psi (Ψ ψ) in LaTeX
Psi is the twenty-third Greek letter. LaTeX writes it as \psi for lowercase and \Psi for uppercase in maths mode; it is best known as the symbol for a quantum-mechanical wave function.
LaTeX command
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In quantum mechanics, the wave function of a system is almost universally written \Psi(x,t) or, for a time-independent state, \psi(x). It appears throughout the Schrodinger equation and anywhere a quantum state needs a symbol, making psi one of the most recognisable Greek letters in physics.
Outside physics, lowercase psi denotes the digamma function, the logarithmic derivative of the gamma function, in mathematics, and the stream function in fluid dynamics. Some probability and set-theoretic texts also use psi as a general-purpose function name once phi and other common letters are taken.
\psi and \Psi have no curly variant form, so there is only one glyph to choose for each case. The main practical hazard is confusing \Psi with \Phi at a glance, since both are tall uppercase Greek letters with a vertical stroke through a rounded body.
Other forms
\psilowercase psi\Psiuppercase psi (Ψ)Examples
$\psi$lowercase psi inline
$\Psi$uppercase psi
$\Psi(x,t)$a time-dependent quantum wave function
$i\hbar \frac{\partial \Psi}{\partial t} = \hat{H}\Psi$the time-dependent Schrodinger equation
Tips and common mistakes
- Uppercase
\Psiis the standard symbol for a full quantum wave function; lowercase\psiis common for a time-independent or single-particle state, but conventions vary by textbook. - There is no
\varpsivariant, unlike phi or theta. - Watch out for confusing
\Psiwith\Phivisually, especially at small font sizes; double check which one your source actually uses. - Combine with accents as needed, for example
\hat{\Psi}for an operator acting on the wave function, or\dot{\psi}for a time derivative.
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What does psi mean in quantum mechanics?
Psi, usually capital \Psi, denotes the wave function of a quantum system, which encodes the probability amplitude for the system's state.
How do I type the wave function symbol in LaTeX?
Use \Psi for the uppercase form, for example , or \psi for lowercase. Both are core LaTeX symbols needing no package.
Is Psi the same as Phi in LaTeX?
No, they are different letters and different commands, \Psi versus \Phi, though their uppercase glyphs can look similar at a glance.
What is the digamma function?
The digamma function, written \psi(x), is the logarithmic derivative of the gamma function, \psi(x) = \Gamma'(x)/\Gamma(x).