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FloridaGators

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The Hamiltonian for a Hydrogen atom in Cartesian Coordinates (is this right?):

[tex]\hat{H} = - \frac{\bar{h}^2}{2m_p}\nabla ^2_p - \frac{\bar{h}^2}{2m_e}\nabla ^2_e - \frac{e^2}{4\pi\epsilon _0r}[/tex]

In Spherical Coordinates do I just use:

x=r sin θ cos φ, y = r sin θ sin φ, and z = r cos θ?

[tex]\hat{H} = - \frac{\bar{h}^2}{2m_p}\nabla ^2_p - \frac{\bar{h}^2}{2m_e}\nabla ^2_e - \frac{e^2}{4\pi\epsilon _0r}[/tex]

In Spherical Coordinates do I just use:

x=r sin θ cos φ, y = r sin θ sin φ, and z = r cos θ?

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