Relativistic De Broglie Relation

[CoreyJKelly]

so I'm trying to derive the De Broglie relation:

$$\lambda$$ = $$\frac{h}{p}$$

for a relativistic particle.. I know that it can be simply written in terms of the relativistic momentum, but to complicate matters, I'm asked to write it in terms of the Kinetic energy.. the expression I'm looking for is:

$$\lambda$$ = $$\frac{h c}{\sqrt{K(K + 2mc^{2})}}$$

I'm getting really close.. but no matter how i manipulate the expressions, i can't seem to get this exact equation... any ideas?

 

[malawi_glenn]

well

$$pc = \sqrt{K^2 + 2Kmc^2}$$

which is derived from:

$$E = K + mc^2$$

And:

$$E^2 = (pc)^2 + (mc^2)^2$$

 

[CoreyJKelly]

haha, i figured it'd be something simple... thanks!