Understanding Conservation of Momentum and Energy in Ideal Quantum Experiments

[ehrenfest]

In the discussion of the ideal quantum experiment and Compton scattering, my book (Shankar page 23) gives these equations for the conservation of momentum and energy:

$$cp' = cp +h-bar(\omega+\omega')$$
$$E' = E +h-bar(\omega-\omega')$$


This experiment involved a photon of known energy and momentum colliding with a particle of unknown energy and momentum.

c is the speed of light, h-bar is h/(2*pi) omega is the frequency of the photon, E is energy, and p is momentum

Can someone please explain how those equations represent the conservation of momentum and energy?

 

[Anonym]

Put glasses on your nose if you need: this is what is written.

Regards, Dany.

 

[ehrenfest]

Why is it $$\omega - \omega'$$ for energy and $$\omega + \omega'$$ for momentum?

 

[ehrenfest]

I see the photon is moving at first and right-moving after the collision and p and p' are only the modulus of the momentum.