Converting equations in Natural units to SI?

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This discussion focuses on converting equations from natural units, where hbar and c are set to 1, to SI units. The key method involves multiplying values by appropriate powers of hbar and c to achieve the correct units. For instance, to convert 1 MeV to mass, one uses the relation 1 MeV/c², and for time, the conversion is hbar/MeV. The conversation also addresses specific terms in dispersion relations, emphasizing the need to multiply linear terms in k by hbar*c to maintain dimensional consistency.

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lordkelvin
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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?
 
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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.
 
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?
 
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.
 

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