Image »Overlap of Two Wave Functions« download
Sharing and adapting of the illustration is allowed with the reference "Alexander Fufaev (fufaev.org)"
One-dimensional real wave functions \( \class{red}{\mathit{\Psi}} \) and \( \class{blue}{\mathit{\Phi}} \) are shown. The overlap is measured using the inner product (or scalar product) \( \langle\class{blue}{\mathit{\Phi}} | \class{red}{\mathit{\Psi}} \rangle \):
- If the inner product is \( \langle\class{blue}{\mathit{\Phi}} | \class{red}{\mathit{\Psi}} \rangle = 1 \), then the corresponding wave functions \( \class{blue}{\mathit{\Phi}} \) and \( \class{red}{\mathit{\Psi}} \) are exactly on top of each other.
- If the inner product is \( \langle\class{blue}{\mathit{\Phi}} | \class{red}{\mathit{\Psi}} \rangle = 0 \), then the wave functions \( \class{blue}{\mathit{\Phi}} \) and \( \class{red}{\mathit{\Psi}} \) do not overlap at all.
- All values of the inner product \( \langle\class{blue}{\mathit{\Phi}} | \class{red}{\mathit{\Psi}} \rangle \) between 1 and 0 result in a partial overlap of the two states.
