Radial Wave Function

#Physics

$\displaystyle u(r)\equiv rR(r)\rightarrow -\frac{\hbar ^{2}}{2m}\frac{\mathrm{d}^2 u}{\mathrm{d} r^{2}}+V_{\text{effective}}u=Eu$

• Radial equation which may be used to solve for $\displaystyle R(r)$, the radial wave function

$\displaystyle V_{\text{effective}}=V+\frac{\hbar ^{2}}{2m} \frac{l(l+1)}{r^{2}}$

• The second term is called the centrifugal term, which has the effect of pushing the particle away from the origin