Completeness relation

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

jtbell
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

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