Theorists frequently use convenient units like $\hbar=1$ or $m=2$ or whatever is useful to simplify the notation in the problem. And after all the calculations are done the units are recovered based on what the unit of the answer needs to be.
I can definitely see why those units are convenient, but I really don't feel comfortable with the recovering step. So far I have only seen one example and it is not quite enough. If somebody could provide some examples of how to recover the units that would be great. As for as I understand that should only need to involve the initial assumptions and the final answer.
Or if somebody knows a good explanatory text that would also be very much appreciated.
Are there any caveats/limitations while using convenient units?
To further clarify why I am confused about this entire procedure:
- Let's assume that I have a problem involving a trap length $L$ and a wave length $\lambda_0$. For convenience I set $L=1$ and $\lambda_0=1$. My final answer needs to be in dimensions of meters. How do I know whether my final answer is supposed to be multiplied by $L$ or divided by $\lambda_0$?
- Lets say I need my final answer in units of angular momentum times capacitance per volume (just as purely hypothetical example). And I started of by setting constants like $\epsilon_0=1$,$L=1$(some length scale),$p0=1$(some momemtum scale). This problem is easy enough that I can still figure it out. But what if I had to deal with constants like the bohr magneton or the conductance quanta. It could become very hard to figure out how I need to combine certain constants to produce the right units. Especially once the number of constants increases. Is there some kind of procedure one can follow that will always spit out the right combination of constants?