Does mean velocity equal group velocity of wave packets in QM?

[fxdung]

Does mean velocity of particle equal group velocity of wave packet in QM?If they do not equal which of them is classical velocity?

 

[Keith_McClary]

What do you mean by "mean velocity of particle" ?
For a particle in free space, you can infer that the group velocity is the same as the classical velocity from Ehrenfest's theorem, but that does not work for more general systems.

 

[fxdung]

It mean <v>=Sum of v*probability of given v

 

[Keith_McClary]

Sum of v*probability of given v

$m \times$ the expectation value of $k$, the Fourier transform of $x$ ?

 

[fxdung]

As your teaching Ehrenfest theorem: mxd/dt<r>=<P>,now I can understand group velocity equal mean velocity and equal classical velocity.

 

[vanhees71]

The expectation value is given by the operator of the quantity you want to calculate the expectation value for. The velocity operator (in the Schrödinger picture) is given by
$$\hat{\vec{v}}=\frac{1}{\mathrm{i} \hbar} [\hat{\vec{x}},\hat{H}].$$
For a usual simple Hamiltonian
$$\hat{H}=\frac{1}{2m} \hat{\vec{p}}^2+V(\hat{x})$$
you get
$$\hat{\vec{v}}=\frac{1}{m} \hat{\vec{v}}.$$