# Single slit momentum conserved ?

If you send an electron through a thin slit it defracts because of the uncertainty principle. But if it has a new velocity not parallel with the direction of travel it had when it entered the slit, then certainly momentum was not conserved.

Can someone please point out what is wrong with the above description.

ZapperZ
Staff Emeritus
Originally posted by Palpatine
If you send an electron through a thin slit it defracts because of the uncertainty principle. But if it has a new velocity not parallel with the direction of travel it had when it entered the slit, then certainly momentum was not conserved.

Can someone please point out what is wrong with the above description.

This is an excellent question, and if you're a physics student, it clearly shows that you are thinking along the way and not just absorbing things blindly. If you're not a physics student, nor a physicist, then you should be! :)

The "slit" here is equivalent to a position-measuring device. It means that the slit interacts with the electron. This interaction causes the "scattering" of the electron into various angle perpendicular to the orientation of the slit. So you can think of the extra momentum that the electron has as being due to this interaction.

A excellent derivation of interference effects in QM that really does not depend on "wave properties" of photons, electrons, etc is by T. Marchella Eur. J. Phys. v.23, p.617 (2002). There are no "wave-particle duality" in QM. It is described by ONE, SINGLE consistent theory. There are only wave-particle duality when we insist that things can only be one or the other, as in our classical world.

Zz.

the fact that the electron goes through the slit (which is at a defenite position (say x-position) along the screen containing the slit) means that the electron is in a state of defenite x-position
...therefore it is not in a state of defenite x-momentum, according to the uncertainity principle...

well, if the electron is not in a defenite state of x-momentum, how do you expect the x-momentum to be conserved?! ...for, what value of momentum would be conserved (if it is to be conserved), because the electron is in a superposition of momentum states and not in a defenite momentum state!

conservation of momentum does not make sense when you're not talking about a defenite momentum state!

the electron initially need not be in a state of defenite x-position...then it is said to be brought to the defenite x-position state through the interaction with the slit-walls...you may think of this interaction as force if you wish...and when a force is acting, momentum is not conserved, is it?

but the crux of the matter is that the electron is not in a defenite momentum state,to begin talking about momentum being conserved!

hope this clears up things.

Stingray

Originally posted by ZapperZ
T. Marchella Eur. J. Phys. v.23, p.617 (2002)

This doesn't work. Could you check the reference?

ZapperZ
Staff Emeritus