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## Homework Statement

Just need to know if i have derived this correctly.

## Homework Equations

## The Attempt at a Solution

Taken the dimensions of the square of the mass-energy formula, and applying the equation to both sides (even though approximated) the equation of [tex]\frac{\lambda}{hf}[/tex] which in this case is also squared, which yields [tex]h^2c^2[/tex] Strictly using Natural Units, is then state:

[tex]h^2c^2(E^2) \approx \lambda^2 E^2(M^2c^4)[/tex]

Now by simple derivation, divide both sides by the wavelength [tex]\lambda[/tex], so that

[tex]\frac{h^2}{\lambda}\frac{c^2}{\lambda}\frac{(E^2)}{\lambda} \approx \frac{\lambda^2}{\lambda}\frac{E^2}{\lambda}(\frac{M^2c^4}{\lambda})[/tex]

which gives numerically:

[tex]E^2(\frac{M^2c^4}{\lambda})=\lambda E^2[/tex]

since [tex]E=\frac{hc}{\lambda}[/tex] and also because [tex]\frac{\lambda^2}{\lambda}\frac{E^2}{\lambda}[/tex] reduces to [tex]\lambda E^2[/tex].

And finally, using the same equations, instead of dividing the derivation by the wavelength, i divided it by [tex]2\pi[/tex], and the result was in this expression:

[tex]\hbar^2c^2\frac{E}{2 \pi}[/tex]

Cheers in advance!

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