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## Homework Statement

How does one use the equations for the conservation of momentum and energy (see my last post in this forum)

[tex] cp' = cp +\hbar(\omega+\omega') [/tex]

[tex] E' = E +\hbar(\omega-\omega') [/tex]

to derive the following

[tex] cp = -(\hbar\omega + \hbar\omega')/2 + sqrt(1+(m^2c^4/(h-bar\omega\omega')) (\hbar\omega - \hbar\omega')/2) [/tex]

and

[tex] cp = (\hbar\omega + \hbar\omega')/2 + sqrt(1+(m^2c^4/(h-bar\omega\omega')) (\hbar\omega - \hbar\omega')/2) [/tex]

## Homework Equations

with Einstein's equation [tex] E^2 = (cp)^2 + (mc^2)^2 [/tex]

## The Attempt at a Solution

I got to a quadratic equation with

a = 4*omega*omega'

b = 4*\hbar*(omega*omega')(omega + omega')

c = 4*\hbar^2*omega^2*omega'^2 - m^2*c^4*(omega - omega')^2 but that does not work. If I work backwards, I get something that is very close to this except without the first term in c. But I double-checked everything and could not find any mistakes.

By the way, how can I make those h-bar's with TeX syntax?

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