## Coefficients of a wave function expansion

This means that if the coefficients $$C_{p\lambda}$$ belong to a unitary or orthogonal trasformation (using the Dirac bra-ket notation) $$\vert p\rangle = \sum_{\lambda} C_{p\lambda}\vert\lambda\rangle,$$ orthogonality is preserved, that is $$\langle \alpha \vert \beta\rangle = \delta_{\alpha\beta}$$ and $$\langle p \vert q\rangle = \delta_{pq}$$.

This propertry is extremely useful when we build up a basis of many-body Stater determinant based states.

Note also that although a basis $$\vert \alpha\rangle$$ contains an infinity of states, for practical calculations we have always to make some truncations.