I need to take the [itex]\nabla^2[/itex] of [itex]x^2+y^2+z^2[/itex]. This is how far I got(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\begin{gather*}

\nabla^2 = \frac{d^2}{dr^2} + \frac{2}{r} \frac{d}{dr} + \frac{1}{r^2}(\frac{1}{sin^2\theta}\frac{d^2}{d\Phi^2} + \frac{1}{sin\theta}\frac{d}{d\theta} sin\theta\frac{d}{d\theta})\\

\nabla^2(r^2sin^2\theta cos^2\Phi + r^2sin^2\theta sin^2\Phi + r^2cos^2\theta = \frac{1}{sin\theta} \frac{d}{d\theta}(sin\theta \frac{d}{d\theta}) + \frac{1}{sin^2\theta} \frac{d^2}{d\Phi^2})

\end{gather*}

[/tex]

Also, can degeneracy occur with n not in order? Like for a part. in 3D box can degeneracy occur for [tex]\Psi_{1,3,5}[/tex] [tex]\Psi_{5,3,1}[/tex] or do the n have to be next each other like [tex]\Psi_{1,2,1}[/tex] [tex]\Psi_{2,1,1}[/tex]?

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# Homework Help: Laplacian in Polar Cooridinates

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