Conceptual question about wavefunctions/momentum

[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)

 

[ZapperZ]

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)

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.

 

[olgranpappy]

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.

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

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

 

[tomasko789]

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)

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.

 

[Phylla]

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.

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