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How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

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- Thread starter cryptist
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- #1

- 121

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How can I solve hydrogen atom with discrete nonlinear schrödinger equation? Could you help me with the mathematics of that, please?

- #2

fzero

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- #3

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- #4

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Gravitational forces between a proton and electron? I realize that both do exert such a field, but at those distances it's a non-issue. Sounds like you want to screw in a nail.

- #5

tom.stoer

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So there is no need for nonlinearity? Then, how should be the discrete formula?

- #7

tom.stoer

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[tex]U_C(r) = -\frac{e^2}{4\pi\epsilon_0}\frac{1}{r}[/tex]

Now you add the potential according to Newton's law of gravitation

[tex]U_N(r) = -Gm_em_p\frac{1}{r}[/tex]

The total potential energy then reads

[tex]U(r) = -\left(\frac{e^2}{4\pi\epsilon_0} + Gm_em_p\right)\frac{1}{r} = -\frac{e^2}{4\pi\epsilon_0} \left(1 + \epsilon\right)\frac{1}{r}[/tex]

This results in a rescaling of the energy levels due to the term

[tex]\epsilon = \frac{4\pi\epsilon_0Gm_em_p}{e^2}[/tex]

- #8

alxm

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Even if you did this correction, what would you compare it to? There are no measurements of electronic states that are anywhere near that accurate. As far as I know, the electronic levels of hydrogen have already been calculated to well within today's experimental accuracy without taking gravity into account. There isn't much point in improving the model if you don't have anything to test it against.

- #9

tom.stoer

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