Classical Formulas

This Paper

Kinetic Energy

$K_{cl}=\frac{1}{2}{m}_0{v}^2.$ Equation (2)

$K_{cl}=\frac{p_{cl}^2}{2m_0}.$ Equation (3)

$K_{re}=m{c}^2-m_0{c}^2.$ Equation (6)

$K_{re}=\frac{p_{re}^2}{m_0+m}.$ Equation (8)

Momentum

$p_{cl}=m_{0}v.$ Equation (3)

$p_{re}=mv.$ Equation (12)

Energy Levels of a Hydrogen Atom

$E_{\mathrm{BO},n}=-K_{cl,n}.$ Equation (26)

$E_{\mathrm{BO},n}=-\frac{{\alpha }^2{m}_e{c}^2}{2n^2},n=1,2,\cdot \cdot \cdot .$ Equation (26)

$E_{\mathrm{SU},n}=-K_{\mathrm{re},n}.$ Equation (29)

$E_{\mathrm{SU},n}=m_e{c}^2\left[{\left(\frac{n^2}{n^2+{\alpha }^2}\right)}^{1/2}-1\right],n=0,1,2,\cdot \cdot \cdot .$ Equation (33b)