TeXipedia

rang

Represents the right angle bracket (⟩) commonly used in mathematical notation for inner products, bra-ket notation, and set builder notation.

Overview

Essential in advanced mathematics and quantum mechanics, particularly for denoting the closing part of angle bracket pairs.

  • Fundamental in quantum mechanics for bra-ket notation representing quantum states
  • Used in linear algebra for inner products and vector spaces
  • Appears in set theory for denoting sequences or ordered sets
  • Often paired with \langle to create enclosing delimiters
  • Common in theoretical physics and advanced mathematical proofs

Examples

Denoting the expectation value of a quantum mechanical operator.

⟨ψ∣A∣ψ⟩=5\langle \psi | A | \psi \rangle = 5 
\langle \psi | A | \psi \rangle = 5

Representing a quantum state bra-ket notation.

∣ψ⟩=α∣0⟩+β∣1⟩|\psi\rangle = \alpha|0\rangle + \beta|1\rangle 
|\psi\rangle = \alpha|0\rangle + \beta|1\rangle

Expressing an inner product in a Hilbert space.

⟨u,v⟩=∑i=1nuivi\langle u,v \rangle = \sum_{i=1}^n u_i v_i 
\langle u,v \rangle = \sum_{i=1}^n u_i v_i