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Display information for equation id:math.1681.8 on revision:1681

* Page found: Das Wasserstoffatom (eq math.1681.8)

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Das Wasserstoffatom Eq: math.1681.8

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TeX (original user input):

\begin{align}

& -\frac{{{\hbar }^{2}}}{2{{m}_{1}}}{{\Delta }_{1}}-\frac{{{\hbar }^{2}}}{2{{m}_{2}}}{{\Delta }_{2}}=-\frac{{{\hbar }^{2}}}{2}\left\{ \frac{{{m}_{1}}}{{{M}^{2}}}{{\Delta }_{R}}+\frac{2}{M}{{\nabla }_{R}}{{\nabla }_{r}}+\frac{1}{{{m}_{1}}}{{\Delta }_{r}}+\frac{{{m}_{2}}}{{{M}^{2}}}{{\Delta }_{R}}-\frac{2}{M}{{\nabla }_{R}}{{\nabla }_{r}}+\frac{1}{{{m}_{2}}}{{\Delta }_{r}} \right\} \\

& -\frac{{{\hbar }^{2}}}{2{{m}_{1}}}{{\Delta }_{1}}-\frac{{{\hbar }^{2}}}{2{{m}_{2}}}{{\Delta }_{2}}=-\frac{{{\hbar }^{2}}}{2M}{{\Delta }_{R}}-\frac{{{\hbar }^{2}}}{2m}{{\Delta }_{r}} \\

\end{align}

TeX (checked):

{\begin{aligned}&-{\frac {{\hbar }^{2}}{2{{m}_{1}}}}{{\Delta }_{1}}-{\frac {{\hbar }^{2}}{2{{m}_{2}}}}{{\Delta }_{2}}=-{\frac {{\hbar }^{2}}{2}}\left\{{\frac {{m}_{1}}{{M}^{2}}}{{\Delta }_{R}}+{\frac {2}{M}}{{\nabla }_{R}}{{\nabla }_{r}}+{\frac {1}{{m}_{1}}}{{\Delta }_{r}}+{\frac {{m}_{2}}{{M}^{2}}}{{\Delta }_{R}}-{\frac {2}{M}}{{\nabla }_{R}}{{\nabla }_{r}}+{\frac {1}{{m}_{2}}}{{\Delta }_{r}}\right\}\\&-{\frac {{\hbar }^{2}}{2{{m}_{1}}}}{{\Delta }_{1}}-{\frac {{\hbar }^{2}}{2{{m}_{2}}}}{{\Delta }_{2}}=-{\frac {{\hbar }^{2}}{2M}}{{\Delta }_{R}}-{\frac {{\hbar }^{2}}{2m}}{{\Delta }_{r}}\\\end{aligned}}

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\begin{aligned} - \frac{ℏ^{2}}{2 m_{1}} Δ_{1} - \frac{ℏ^{2}}{2 m_{2}} Δ_{2} = - \frac{ℏ^{2}}{2} {\frac{m_{1}}{M^{2}} Δ_{R} + \frac{2}{M} \nabla_{R} \nabla_{r} + \frac{1}{m_{1}} Δ_{r} + \frac{m_{2}}{M^{2}} Δ_{R} - \frac{2}{M} \nabla_{R} \nabla_{r} + \frac{1}{m_{2}} Δ_{r}} \\ - \frac{ℏ^{2}}{2 m_{1}} Δ_{1} - \frac{ℏ^{2}}{2 m_{2}} Δ_{2} = - \frac{ℏ^{2}}{2 M} Δ_{R} - \frac{ℏ^{2}}{2 m} Δ_{r} \end{aligned}

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Identifiers

$m_{1}$

$Δ_{1}$

$m_{2}$

$Δ_{2}$

$m_{1}$

$M$

$Δ_{R}$

$M$

$R$

$r$

$m_{1}$

$Δ_{r}$

$m_{2}$

$M$

$Δ_{R}$

$M$

$R$

$r$

$m_{2}$

$Δ_{r}$

$m_{1}$

$Δ_{1}$

$m_{2}$

$Δ_{2}$

$M$

$Δ_{R}$

$m$

$Δ_{r}$

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