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.

 

[pmacias]

I can understand your confusion and difficulty in converting equations in natural units to SI units. The process of converting equations from one set of units to another can be complex and requires a strong understanding of the underlying physical principles.

One approach to convert equations in natural units to SI units is to use dimensional analysis. This method involves identifying the fundamental quantities and their dimensions in both sets of units and using conversion factors to transform the equation. For example, in natural units, hbar and c both have dimensions of energy multiplied by length, while in SI units, hbar has dimensions of energy multiplied by time and c has dimensions of length divided by time. By using appropriate conversion factors, you can convert these quantities to their SI unit equivalents.

Another approach is to use the relationship between natural units and SI units. In natural units, hbar and c are set to 1, meaning that the units of these quantities are not explicitly written in equations. However, in SI units, hbar and c have well-defined values and units. By using the relationship hbar = h/2π and c = 299,792,458 m/s, you can convert an equation from natural units to SI units.

It is important to note that there is no one general method for converting equations from natural units to SI units. The approach will depend on the specific equation and the quantities involved. It is always recommended to double-check your conversions and units to ensure the accuracy of your results.

I hope this response helps you in converting equations in natural units to SI units. If you have any further questions or need clarification, please do not hesitate to ask.