Function elem_charge_squared_f (o2scl_const)

O2scl : Function List

template<class fp_t>
fp_t o2scl_const::elem_charge_squared_f()

Electron charge squared in SI(MKS) units (derived)

In MKS units:

\[\begin{split}\begin{eqnarray*} &\vec{\nabla} \cdot \vec{E} = \rho \, , \quad \vec{E}=-\vec{\nabla} \Phi \, , \quad \nabla^2 \Phi = - \rho \, , &\\& F=\frac{1}{4 \pi \varepsilon_0}\frac{q_1 q_2}{r^2} \, , \quad W=\frac{1}{2} \int \rho V d^3 x =\frac{\varepsilon_0}{2} \int | \vec{E} |^2 d^3 x \, , \quad \alpha=\frac{e^2}{4 \pi \varepsilon_0 \hbar c}=\frac{1}{137}& \end{eqnarray*}\end{split}\]

Note the conversion formulas

\[ q_HL=\sqrt{4 \pi} q_G = \frac{1}{\sqrt{\varepsilon_0}} q_{SI} \]

as mentioned, e.g. in pg. 13 of D. Griffiths Intro to Elem. Particles.