# Quick QM question(s)

1. Oct 9, 2012

### Beer-monster

I'm trying to "sure"up my Quantum Mechanics and found an sheet of mostly conceptual review questions. A sort of "Quantum minima".

I'd like to check my answers to a couple of these.

Firstly:

In terms of state vector the wavefunction is the expansion coefficient (probability amplitude) of a state i.e

$$\psi = \langle x \left | \psi \right\rangle$$

What happens if you put an operator (e.g. p) between the bra and ket as if you were calculating an expectation value? i.e.

$$\left\langle x \left | p \right | \psi \right \rangle$$

My guess is that the action of the operator on the state vector $\left|\psi\right\rangle$ will collapse the vector to a single basis vector of p $\left| p \right\rangle$ the expression above would reduce to an element of a basis transformation matrix $\left\langle x | p \right\rangle$

Is that correct...at least in part?

Last edited: Oct 9, 2012
2. Oct 9, 2012

### dextercioby

Not quite. The action of p on the ket psi leads to a ket phi, generally different. Then the matrix element with the bra x leads to a complex number, namely phi(x).

3. Oct 10, 2012