|
<math>\Psi\,\left (r,\theta,\phi \right)=R_{n}(r)\Theta_{l,m_l}(\theta)\Phi_{m_l}(\phi)</math>
<table border=0 cellspacing=0 cellpadding=0 width="90%" align=center class="equation"><tr>
<td width="10%"></td>
<td nowrap><i> Ψ(r,θ,φ)</i> = </td>
<td nowrap> <i> R<sub>n</sub>(r)*Θ<sub>l,ml</sub> (θ)*Φ<sub>ml</sub>(φ)</i></td>
<td width="50%"></td>
<td nowrap>(1)</td>
</tr></table>
<table border=0 cellspacing=0 cellpadding=0 width="90%" align=center class="equation"><tr>
<td width="10%"></td>
<td nowrap><i>Φ<sub>ml</sub>(φ)</i> = </td>
<td nowrap align=center><i>1</i><hr noshade size=1><i>sqrt(2 π)</i></td>
<td nowrap> <i>e<sup>i m<sub>l</sub> φ </sup></i></td>
<td nowrap> <i></i></td>
<td width="50%"></td>
<td nowrap>(2)</td>
</tr></table>
<math>\Phi_{m_l}(\phi)=\frac{1}{\sqrt{2\pi}}e^{i m_l \phi}</math>
<table border=0 cellspacing=0 cellpadding=0 width="90%" align=center class="equation"><tr>
<td width="10%"></td>
<td nowrap><i>Θ<sub>l,ml</sub>(θ)</i> = </td>
<td nowrap> <i>P<sub>ml</sub> cosθ</i></td>
<td width="50%"></td>
<td nowrap>(3)</td>
</tr></table>
<table border=0 cellspacing=0 cellpadding=0 width="90%" align=center class="equation"><tr>
<td width="10%"></td>
<td nowrap><i>R<sub>n,l</sub>(r)</i> = </td>
<td nowrap> <i>√</i></td>
<td nowrap align=center><i>n-l-1</i><hr noshade size=1><i>2n(n-1)!</i></td>
<td nowrap> <i>L<sub>n,l</sub>(r)</i></td>
<math>\Theta_{l m_l}(\theta)=P_{m_l}\cos\theta</math>
<td nowrap align=center><i>e<sup>-ρ</sup></i><hr noshade size=1><i>2 n</i></td>
<td width="50%"></td>
<td nowrap>(4)</td>
</tr></table>
<table border=0 cellspacing=0 cellpadding=0 width="90%" align=center class="equation"><tr>
<math>R_{n l}(r)=\sqrt(\frac{n+1}{2n(n-1)!})L_{n l}(r)\frac{e^{-\rho}}{2n}</math>
<td width="10%"></td>
<td nowrap><i>E</i> = </td>
<td nowrap align=center><i>-me<sup>4</sup></i><hr noshade size=1><i>8 m<sub>e</sub> π<sup>2</sup> ε<sub>0</sub><sup>2</sup> ħ<sup>2</sup></i></td>
<math>E=\frac{m_e e^4}{32 \pi^2 \epsilon_0^2 h^2} \frac{1}{n^2}</math>
<td nowrap align=center><i>1</i><hr noshade size=1><i>n<sup>2</sup></i></td>
<td width="50%"></td>
<td nowrap>(5)</td>
</tr></table>
| 