I have been given these 4 eigenfunctions of the hydrogen atoms first 2 n-shells.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \psi_{100}(r, \theta, \phi )=\frac{1}{\sqrt{\pi a^3_0}}e^{-r/a_0} [/tex]

[tex] \psi_{200}(r, \theta, \phi )=\frac{1}{\sqrt{8\pi a^3_0}}(1-\frac{r}{2a_0})e^{-r/2a_0} [/tex]

[tex] \psi_{210}(r, \theta, \phi )=\frac{1}{4\sqrt{2\pi a^3_0}}(\frac{r}{a_0})e^{-r/2a_0} cos\theta[/tex]

[tex] \psi_{21\pm 1}(r, \theta, \phi )=\pm\frac{1}{8\sqrt{\pi a^3_0}}(\frac{r}{a_0})e^{-\frac{r}{2a_0}} sin\theta e^{\pm i\phi}[/tex]

Where [tex] a_0 [/tex] is the Bohr radius.

I am suposed to show that the superposition

[tex] |\psi_{nlm}(r, \theta, \phi )|^2 [/tex] is sphericaly symmetric within each shell.

Now what I dont know is how do I show spherical symmetri(not even generaly and not just in this particular case). Any hints?

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# Homework Help: Spherical symmetri of eigenfunctions?

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