4 ms·

The article fails to explain where the 2*pi comes from, and why 1/alpha is more natural. Does this quantity arise in some context other than unit-analysis specu

• noobermin 11y ago
  h-bar[0]: [0] https://en.wikipedia.org/wiki/Planck_constant https://en.wikipedia.org/wiki/Planck_constant
• jeffwass 11y ago
  The 2pi comes from the usual method of using hbar, instead of h. Where hbar = h/2pi, and is the Planck constant adjusted to use radians instead of cycles. This is much more natural when working with frequencies instead of using cycles. Yes, this constant arises prolifically when looking at the atomic "fine structure", which modifies the usual hydrogen energies to includes interactions between an electron's spin and its orbit (the un-modified ones only include the kinetic energy of the reduced electron-proton and the electric potential energy). There are further interactions that can be added, eg the hyperfine interaction which includes the spin-spin interaction between the proton in the nucleus and the orbiting electron. And if you use Planck units where hbar=c=G=1, you can do many things easily, for example denote the potential of an electron at distance r as just alpha/r (without all those other pesky constants embedded in Gauss's law).
• jessriedel 11y ago
  jeffwas has explained the factor of 2pi. It's just the 2pi radians in a circle to convert from angular frequencies to regular frequencies. I don't know the detailed history, but in practice the fact that it's an inverse is essentially because it's most important role is as part of an expansion like a Taylor series. The standard method for calculating lots of observable effects gives an answer with the form X = X_0 + \alphaX_1 + \alpha^2X_2/2! + ...