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6.1: Атом водню
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\[ \nabla^{2} = \frac{1}{r}\frac{d^{2}}{dr^{2}}+\frac{1}{r^{2}}\frac{1}{sin^{2}\theta}\frac{d^{2}}{d\phi^{2}}+\frac{1}{r^{2}}\frac{1}{sin\theta}\frac{d}{d\theta}sin\theta \frac{d}{d\theta} \nonumber \... $\nabla^{2} = \frac{1}{r}\frac{d^{2}}{dr^{2}}+\frac{1}{r^{2}}\frac{1}{sin^{2}\theta}\frac{d^{2}}{d\phi^{2}}+\frac{1}{r^{2}}\frac{1}{sin\theta}\frac{d}{d\theta}sin\theta \frac{d}{d\theta} \nonumber$ $= -\frac{\hbar^{2}}{2m} \left( \frac{1}{r}\frac{d^{2}}{dr^{2}}r +\frac{1}{r^{2}}\frac{1}{sin^{2}\theta}\frac{d^{2}}{d\phi^{2}}+\frac{1}{r^{2}}\frac{1}{sin \theta}\frac{d}{d\theta}sin\theta \frac{d}{d\theta} \right) - \frac{Zq^{2}}{4\pi\epsilon_{0}r}$