Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Completeness relation

  1. Oct 13, 2013 #1
    hi, in quantum physics completeness relation is often use it equals to one - what is its significance in multiplying with state vector . thanks
  2. jcsd
  3. Oct 13, 2013 #2


    User Avatar

    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

    $$\psi(x) = \sum {c_n \psi_n(x)}$$
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook