# Electron's mean momentum

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1. Mar 15, 2015

### valle29

Having calculated that the momentum uncertainty, Δp, for an electron confined in a 1 dimensional box of a width, 10-15 m equivalent to a typical nuclear diameter, is (5.2x10^-20 [kg m s-1] )
Knowing also that nuclei often emit electrons with energies between 1 and 10 MeV.

How do I calculate the electron's mean momentum?

thank you.

2. Mar 15, 2015

### jfizzix

If we're assuming this 1D box has infinite walls, or that the energy of the electron is small enough so that it is in a bound state of a box with finite walls, then the answer is remarkably simple:

If the electron's position probability density doesn't change in time, then its mean position is constant in time.
If the electron's mean position is constant, then Ehrenfest's theorem tells us that the mean momentum must be zero.

If the electron is not in a bound state, you could calculate the mean momentum in at least three ways:
-using the position-space wavefunction
-using the momentum-space wavefunction
-using the mean position and Ehrenfest's theorem