Single slit momentum conserved ?

In summary: 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...according to the uncertainty principle......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!
  • #1
Palpatine
28
0
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.
 
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  • #2
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.
 
  • #3
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.
 
  • #4


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

This doesn't work. Could you check the reference?
 
  • #5
Originally posted by Stingray
This doesn't work. Could you check the reference?

Sorry, I had typos there..

http://www.iop.org/EJ/abstract/0143-0807/23/6/303".

Zz.
 
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What is single slit momentum conservation?

Single slit momentum conservation is a principle in physics that states that the total momentum of an isolated system remains constant before and after an event or interaction involving a single slit.

Why is single slit momentum conservation important?

Single slit momentum conservation is important because it helps us understand and predict the behavior of particles before and after they pass through a single slit. It also helps to explain the conservation of energy in these systems.

How does single slit momentum conservation relate to the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle states that the position and momentum of a particle cannot be known simultaneously with absolute certainty. Single slit momentum conservation plays a role in this principle by demonstrating that the momentum of a particle can be altered by interacting with a single slit, making it impossible to know both the position and momentum of the particle with certainty.

What factors can affect single slit momentum conservation?

Some factors that can affect single slit momentum conservation include the mass and velocity of the particles, the angle at which they enter the slit, and the properties of the slit itself (such as its width and shape).

How is single slit momentum conservation applied in real-world situations?

Single slit momentum conservation is applied in various fields, such as optics and quantum mechanics, to study the behavior of particles passing through a single slit. It is also used in engineering and technology, such as in the design of particle accelerators and electron microscopes.

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