Converting equations in Natural units to SI?

lordkelvin

How can I convert an equation in units where hbar = c = 1 into an equation with hbar and c in SI units? I searched around a bit and wasn't able to find anything (I'm probably not asking the right question). Is there some general way to do it rather than just intuition from having seen the equations before with hbar and c in them?

mfb

Simply multiply the value with appropriate powers of hbar and c to get the correct unit.

You have 1MeV as a result and want a mass? It is 1MeV/c^2. You have 1/MeV as result and want a time? It is hbar/MeV. And so on.

lordkelvin

I have a dispersion relation that involves some constants (and it's in natural units so no c or hbar shows up). I'd like to plot E versus k using this equation with k and E in SI units.
There are some terms with k^2/(2m) so I can just multiply those by hbar^2, but then there's another term that is only linear in k which I don't know what to do with. I would like to be able to multiply it by some combo of hbar and c but I have no way of knowing whether it's right. So I have a term that is in units of 1eV of inverse length, what do I multiply by? hbar*c?

mfb

if you have [k/m] = 1/(m*kg), this is not equivalent to an energy with hbar=c=1.
Or do you have a simple k? Well, [k]=1/m, so [k*hbar*c]=1/m Js m/s = J.
Correct, multiply by hbar*c.