# Derive the Compton I'm stuck :[

1. Jan 18, 2009

### latitude

1. The problem statement, all variables and given/known data

Derive the compton equation.

2. Relevant equations
$$\lambda$$ - $$\lambda$$ = h/ mc (1 - cos$$\theta$$)
E = hf = hc/$$\lambda$$

3. The attempt at a solution
Okay, I'm sorry this is so long, I'll try and make it as concise as it is possible for a whole blather of random crap to be :]

Conservation of momentum components:
h/$$\lambda$$ = h/$$\lambda$$(cos$$\theta$$) + Pe(cos$$\psi$$)
0 = h/$$\lambda$$(sin$$\theta$$) - Pe(sin$$\psi$$)

After some combining, squaring, and the like (getting rid of $$\psi$$):
Pe2 = (h/$$\lambda$$)2 - (h/$$\lambda$$)2cos2$$\theta$$ + (h/$$\lambda$$)2sin2$$\theta$$ - (h/$$\lambda$$)(h/$$\lambda$$)cos$$\theta$$

E2 = p2c2 + ER2
So
P2 = (E2 - ER2)/c2

So I plug that into my momentum (I'm not gonna write the righthand side of the equation while i show what I did w/ that)

(E2 - ER2)/c2 = ...
((hc/$$\lambda$$)2 - (mc2)2)/c2 = .
I tried to get rid of the denominator 'c'...
(h/$$\lambda$$)2 - m2c2 = ...

(m2c2$$\lambda$$)/h = $$\lambda$$/$$\lambda$$ - h/$$\lambda$$cos$$\theta$$

After some more fiddling I get to this:

$$\lambda$$` = h/m2c2 - (h/$$\lambda$$)(h/m2c2)cos$$\theta$$

It's kind of close but not really... I can write out all the steps I made if that is necessary, but I'm kind of hoping I made one nice, simple-to-fix error that is glaringly obvious to the more experienced :)

Thank you :)

2. Jan 19, 2009

### tiny-tim

Hi latitude!

(have a lambda: λ and a theta: θ and a psi: ψ )
eugh

the first - should be a +