# Units and the fine structure constant

#### topsquark

Forum Staff
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?

Thanks!

-Dan

#### studiot

Extract from Wiki

Choosing constants to normalize

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
1/137​
, 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 =
kee2/ħc
, where ke is the Coulomb constant, e is the elementary charge, ħ is the reduced Planck constant, and c is the speed of light.

https://en.wikipedia.org/wiki/Natural_units

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