I guess this question can apply in all the generality of the 3D Schrodinger eqn. with a central force, the case I'm thinking of however is the the hydrogen atom.(adsbygoogle = window.adsbygoogle || []).push({});

When solving the equation, we derive the quantization of the angular momentum, which has me thinking that before we begin quantizing it, shouldnt we first ask if it has any angular momentum?

My impression (and it might be wrong) is that if we have an accelerating charge, it must radiate photons and lose energy etc. the reason why this does not happen in the atom is that the electron waves are stationary. Meaning, that the electron does not revolve around the nucleus, rather there are stationary probability waves centered around the nucleus. If that is in fact the case it shouldnt have any velocity since it's not moving

The problem with that is that if it doesnt have velocity then it shouldnt have momentum either (unless it can somehow have momentum without velocity). But if it doesnt then have momentum the wavelength from the de broglie eqn should be infinite.

On the other hand if it does have velocity (and corresponding momentum, wavelength, and angular momentum) shouldnt it also have centripetal acceleration? If that is in fact the case, it seems to me that it is not a stationary wave, rather its an accelerating particle, and should be radiating, losing energy...

How do I make sense of this?

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# Angular momentum in the 3D Schrodinger eqn with a central force

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