Units and the fine structure constant


Forum Staff
Apr 2008
On the dance floor, baby!
I'm (still) working through the Dirac equation solution for the hydrogen atom and I've run across a problem. Apparently I'm working in a system of units where the fine structure constant is equal to 1, not the usual 1/137.

I know that (hbar) = c = 1 and that k = 1/(4 (pi) (epsilon)_0) = 1. Requiring that the fine structure constant = 1 would seem to also set e = 1, but I've never heard of such a system?


Apr 2015
Somerset, England
Extract from Wiki

Choosing constants to normalize[edit]

Out of the many physical constants, the designer of a system of natural unit systems must choose a few of these constants to normalize (set equal to 1). It is not possible to normalize just any set of constants. For example, the mass of a proton and the mass of an electron cannot both be normalized: if the mass of an electron is defined to be 1, then the mass of a proton has to be approximately 1836. In a less trivial example, the fine-structure constant, α
, cannot be set to 1, at least not independently, because it is a dimensionless number defined in terms of other quantities, some of which one may want to set to unity as well. The fine-structure constant is related to other fundamental constants through α =
, where ke is the Coulomb constant, e is the elementary charge, ħ is the reduced Planck constant, and c is the speed of light.