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A question of Quantum

How is momentum conserved on the quantum scale? - Photon/particle interaction...
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[marked-for-expiry] - not an idea, this is just me asking a question... I will delete if/when someone complains and/or if I get an answer...

I was just doing a bit of a thought experiment last night, and was wondering about conservation of momentum during particle/photon interaction. See if anyone can explain this.

Imagine an electron in free space. Our current frame of reference has this electron not moving very fast at all, or even stationary. In comes a photon of energy x, with momentum y (and y isn't a very big number). When the electron absorbs the photon, it will of course gain kinetic energy from the photon. My question is, how can any arbitrary increase of the velocity of the electron satisfy conservation of momentum? The mass of the electron is such that it's corresponding new velocity will result in momentum that the original system didn't have.

Do that experiment again with a much more massive particle. Say a proton or neutron. Once again, I don't understand how momentum can be conserved. Yes, it's a long time since I worried about Q-M.

Are such interactions, (that would not allow momentum to be conserved) specifically disallowed, ie does the particle simply not absorb the photon?

Custardguts, Jun 01 2009

Compton scattering http://en.wikipedia.../Compton_scattering
[xaviergisz, Jun 01 2009]

[link]






       I'm confused by your problem. The electron (which, say, is stationary) absorbs a photon (coming from the left), and then heads off leftward. Where's the problem? Are you assuming that the photon has zero mass?
MaxwellBuchanan, Jun 01 2009
  

       He's assuming that his system initially has zero momentum. Which is false, since the system necessarily includes the photon at the outset. And this photon's momentum is indeterminate, since it hasn't been measured yet. That is, both entities exist in their waveform, and so you can't possibly rule out any initial momentum from the electron, as well.
daseva, Jun 01 2009
  

       No, but because the electron has greater mass than the photon, it can't have the same momentum and kinetic energy. KE is proportional to velocity squared, whereas momentum is proportional to velocity. In a large newtonian inelastic collision, Between a massive slow moving particle and a small energetic one, final velocity is only determined by the sum of momentum, and the excess energy is seen as heat. But an electron, AFAIK, can only absorb energy as kinetic. So where would the extra energy go?
Custardguts, Jun 01 2009
  

       You lost me. What 'extra' energy? I never said it would have the same p or K.E.
daseva, Jun 01 2009
  

       [Daseva] - No, I'm just saying the photon has very small momentum compared to it's energy.
Custardguts, Jun 01 2009
  

       Excellent. Thanks for the link. Yes momentum must be conserved, no electrons can't have energy other than KE. Result: lower energy photon immediately produced to satisfy newtonian physics. It's all very neat.   

       Anyone want this left up for a bit, or should I delete imediately? Someone MFD and I'll make it go away.
Custardguts, Jun 01 2009
  
      
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