1. Mar 17, 2008

noospace

Hi all,

If I have the wave function of a system, then the expectation of position is easily visualized as the centroid of the distribution.

Does anyone know how to visualize the expectation of velocity given just the postion-space wavefunction (real and imaginary parts)

2. Mar 17, 2008

ZapperZ

Staff Emeritus
Er... couldn't you just use the expectation value of the momentum, i.e. <p>? I'm assuming that you know what p operator is in the real-space representation.

Zz.

3. Mar 18, 2008

olgranpappy

I do know what it is!
$$p = -i \frac{d}{dx}$$

...always. since p generates translations in space.

4. Mar 18, 2008

What i'm going to tell you is in a contradiction with your question, cause you say, you only have realspace wavefunction. However, i find it very instrumental to imagine it in this way:

Take the realspace wavefunction. Do its fourier transform. You obtain a k-space wavefunction. In this representation, the momentum (~velocity) operator has exactly the same form as position operator in realspace representation. So the centre of this function is the mean momentum value.

5. Mar 19, 2008

Phylla

yes,I agree this.
Use foiurier transformation to get the wavefunction in the momentum representation.