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Display information for equation id:math.1596.40 on revision:1596

* Page found: Zeitunabhängige Schrödinger- Gleichung und stationäre Zustände (eq math.1596.40)

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\begin{align}
& \int_{{{R}^{3}}}^{{}}{{{\phi }_{m}}*(\bar{r})}{{\phi }_{n}}(\bar{r}){{d}^{3}}r={{\delta }_{nm}}\Rightarrow \sum\limits_{n}{{{c}_{n}}}\int_{{{R}^{3}}}^{{}}{{{\phi }_{m}}*(\bar{r})}{{\phi }_{n}}(\bar{r}){{d}^{3}}r=\sum\limits_{n}{{{c}_{n}}}{{\delta }_{nm}}={{c}_{m}} \\
& \sum\limits_{n}{{{c}_{n}}}\int_{{{R}^{3}}}^{{}}{{{\phi }_{m}}*(\bar{r})}{{\phi }_{n}}(\bar{r}){{d}^{3}}r=\int_{{{R}^{3}}}^{{}}{{{\Psi }_{0}}(\bar{r}){{\phi }_{m}}*(\bar{r}){{d}^{3}}r}={{c}_{m}} \\
\end{align}

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R3ϕm*(r¯)ϕn(r¯)d3r=δnmncnR3ϕm*(r¯)ϕn(r¯)d3r=ncnδnm=cmncnR3ϕm*(r¯)ϕn(r¯)d3r=R3Ψ0(r¯)ϕm*(r¯)d3r=cm
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