# Completeness relation

1. Oct 13, 2013

### wasi-uz-zaman

hi, in quantum physics completeness relation is often use it equals to one - what is its significance in multiplying with state vector . thanks
wasi

2. Oct 13, 2013

### Staff: Mentor

Do you mean this:

$$\sum {| n \rangle \langle n |} = 1\\ \sum {| n \rangle \langle n | \psi \rangle} = | \psi \rangle$$

This represents the expansion of $|\psi\rangle$ into a linear combination of orthonormal basis states $|n\rangle$. The $\langle n | \psi \rangle$ are the coefficients of the expansion. In the position representation we usually write this as something like

$$\psi(x) = \sum {c_n \psi_n(x)}$$