# Relativistic De Broglie Relation

1. Sep 29, 2007

### 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?

2. Sep 29, 2007

### malawi_glenn

well

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

which is derived from:

$$E = K + mc^2$$

And:

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

3. Sep 29, 2007

### CoreyJKelly

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