In physics we frequently encounter with quantities that are 'reduced'. But why? Why there are reduced Planck constant, temperature, pressure etc?
Asked
Active
Viewed 517 times
1 Answers
2
Usually a reduced quantity is a way to rewrite a quantity, in order to make the physical meaning clearer and/or make formulas easier to understand. The reduced Planck constant, for example, allows you to write the angular momentum equations in a particularly clear way \begin{align} J^2 = j(j+1) \hbar^2,\qquad & j = 0, \tfrac{1}{2}, 1, \tfrac{3}{2}, \ldots, \\ J_z = m \hbar, \qquad\qquad\quad & m = -j, -j+1, \ldots, j. \end{align} other examples where the reduced Planck constants make equations more readable are the energy equation ($E = \hbar \omega$) and the Schroedinger's equation.
Regarding the reduced temperature, it's a similar idea. It represents the temperature $T$ as a multiple of critical temperatures $T_c$. \begin{align} T_{red} = \frac{T}{T_c} \end{align} This has the advantage to be $1$ when the temperature is the critical temperature. Another important advantage is that this quantity has no dimension (being a ratio), so it is easier to use in calculations. The argument is very similar for the reduced pressure.
