Ehrenfest theorem and the hydrogen atom

[qsa]

Is there any derivation of the bohr model for hydrogen using Ehrenfest theorem. References are appreciated.

 

[SpectraCat]

Is there any derivation of the bohr model for hydrogen using Ehrenfest theorem. References are appreciated.

The Bohr model was an (incorrect) empirical model based solely on observations (as well as Coulomb's Law), so I doubt there is any "derivation" of it using the Ehrenfest theorem. Also, I am not positive, but I would guess that the Bohr model pre-dates the Ehrenfest theorem by a non-negligible amount.

 

[qsa]

The Bohr model was an (incorrect) empirical model based solely on observations (as well as Coulomb's Law), so I doubt there is any "derivation" of it using the Ehrenfest theorem. Also, I am not positive, but I would guess that the Bohr model pre-dates the Ehrenfest theorem by a non-negligible amount.

Thanks for the reply. of course, your points are correct, but still bohr model gives a good classical approximation. I wounder what happens if one tries, where would you think the difficulty be? They do seem to be related via the Correspondence_principle




http://en.wikipedia.org/wiki/Ehrenfest_theorem

http://en.wikipedia.org/wiki/Correspondence_principle

 

[atyy]

I believe not from the Ehrenfest theorem, but from quantum mechanics.

Take a look at chapters 31 and 34 of http://www.cns.gatech.edu/ChaosBook/. The Bohr-Sommerfeld quantization condition is reached in Eq 34.15.

 

[dextercioby]

The Ehrenfest Theorem is a sharp result proven quite recently (2009/2010) starting from the Schrödinger equation.

It's a mere coincidence that the results of Bohr 1913 were also obtained by Pauli 1925 and Schrödinger 1926, as we now know that Bohr's assumptions are invalid.

There's no derivation of Bohr's assumptions from quantum mechanics.

 

[SpectraCat]

It's a mere coincidence that the results of Bohr 1913 were also obtained by Pauli 1925 and Schrödinger 1926, as we now know that Bohr's assumptions are invalid.

I would disagree with that .. it was more than "mere coincidence". Bohr based his model on empirical observations, and thus *required* that the energy spacing between the atomic levels matched the observed frequencies in the hydrogen spectrum. Thus his hypothesis about the energy levels of the atom being quantized was correct, and (NOT coincidentally) is the only part of his theory that agrees with the "correct" version of the theory developed later.

 

[dextercioby]

Obviously he knew how the lines are distributed in both the visible (Balmer) and invisible spectrum, then he only <fine tuned> his assumptions based on the quantization idea by Planck & Einstein. But nothing more.

 

[SpectraCat]

Obviously he knew how the lines are distributed in both the visible (Balmer) and invisible spectrum, then he only <fine tuned> his assumptions based on the quantization idea by Planck & Einstein. But nothing more.

In my opinion, that is a gross trivialization of Bohr's contribution to the development of QM and atomic theory. It's true that many of the approaches and ideas incorporated into "old QM" turned out to be incorrect to one degree or another, but at the very least, "old QM" provided a foil for the subsequent development of correct QM theories.