Timeline for Why did the Bohr Model Successfully calculate some of the energy levels in hydrogen?
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| Nov 6, 2019 at 18:10 | comment | added | Frederic Thomas | There is one thing you can do: Take Schrodinger's equation Set $\psi =a e^{i\frac{J}{\hbar}}$ in. One will get an equation for $a$ and for $J$ higher order terms of $\hbar$ like $\hbar^2$ are to be neglected. Then you get the Hamilton-Jacobi-equation (HJE) With the HJE you can compute the Bohr's model. So one kind of develops Schrodinger's equation in orders of $\hbar$ and one gets a fundamental classical mechanics equation which can be used for getting Bohr's model (adding the quantisation principle). | |
| Nov 6, 2019 at 17:58 | comment | added | Frederic Thomas | With the difference that GR is still classical physics, not QM. You are kind of right, you won't find an "derivation" of Bohr's model from QED, because such a derivation does not exist. Bohr's model is incomplete, it cannot explain chemical bonding. It cannot explain Pauli's principle, so it just tries to explain a detail of a very large phenomology of microscopic physics. People like Heisenberg already knew, otherwise he would not have searched for a better theory. | |
| Nov 6, 2019 at 17:37 | comment | added | Stefan | With GR you can explain why newtons theory of gravity worked so well for 200 years. It's the same understanding that I search for regarding this question. Maybe it was all just luck. | |
| Nov 6, 2019 at 17:29 | comment | added | Frederic Thomas | It a kind of change of paradigma. Again, Bohr's theory is based on classical mechanics, and wave mechanics on QM. Today everything is explained by QM, it is the more comprehensive theory. And again, Bohr cannot do everything. But QM can. | |
| Nov 6, 2019 at 17:24 | comment | added | Stefan | Thanks. I agree on the shortcommings as I studied QM atom physics and got some exposure to relativistic QM. But as you say the agreement is amazing for a theory that is abonnded and I was wondering if there is a deep results that could shed light on why's so. I got a clue on the internet that such results exists but was unable to find it. | |
| Nov 6, 2019 at 17:17 | history | answered | Frederic Thomas | CC BY-SA 4.0 |