Originally Posted by **studiot** As I understand it, there is only one wave function. |

The terminology can be tricky. Normally if you see the term

**wave function** without a qualifier then it refers to the position representation of the quantum state $\displaystyle |\Psi(x, y, z, t)>$. Otherwise one speaks of the wave function in the

*q* representation where

*q* is an observable such as position, momentum, energy, etc.

Originally Posted by **studiot** Momentum is derived by applying the momentum operator as a premultiplier. |

In quantum mechanics there are various terms which refer to momentum:

(1) Momentum operator,

**P**.

(2) Eigenvalues of momentum operator,

*p*.

(3) Expectation of momentum, <p>.

Momentum eigenvalues are what are measured in the lab. To find these eigenvalues of

**P** apply it to the wave function and the following will result

**P**$\displaystyle \Psi$ =

*p*$\displaystyle \Psi$

As you an see one simply applies

**P** to $\displaystyle \Psi$ and will result multiplied by a constant. That constant is the momentum eigenvalue.

Originally Posted by **studiot** Yes, MBW, momentum and position are linked since one is the Fourier transform of the other. |

It's the momentum representation and position representation of the wave function which are Fourier transform pairs, not momentum itself.