Bohr model for electron energy states

[Iceking20]

TL;DR

What parts of bohr model for electron energy states are still valid?

I know that we use quantum mechanic and wave function to calculate probability of finding electrons but is there anything valid about bohr model that we still use it?

 

[mfb]

The energy levels are still reasonable approximations for hydrogen-like atoms.

 

[vanhees71]

Where is the Bohr-Sommerfeld quantization still used? I consider it interesting to understand the historical development of modern quantum mechanics, but it should not be taught anymore in introductory physics lectures on quantum mechanics since it's not only quantitatively wrong but provides utterly wrong qualitative pictures which you have to eliminate from your thinking again when learning the modern theory. The most difficult part of learning modern QT is to unlearn classical concepts, and thus it's good to omit at least classical pictures where they are really failing, and this is precisely the case with the Bohr-Sommerfeld quantization prescription.

 

[A. Neumaier]

Where is the Bohr-Sommerfeld quantization still used?

A lot of useful semiclassical physics is done based on Bohr-Sommerfeld quantization. In particular, modern versions of it are indispensable in the spectroscopy of large molecules, where the more accurate ab initio methods become numerically too demanding.

• Norcliffe, A., & Percival, I. C., Correspondence identities II. The Bohr-Sommerfeld identity for the hydrogen atom. Journal of Physics B: Atomic and Molecular Physics, 1 (1968), 784.
• Colwell, S. M., & Percival, I. C., The semiclassical determination of potential surfaces from observed spectra. I. Chemical Physics, 75 (1983), 215-223.

It is also used for meson spectra in constituent quark models: https://arxiv.org/pdf/hep-ph/0412170
and for the analysis of black holes: https://arxiv.org/pdf/1204.1699
to mention just a few more recent uses.

 

[A. Neumaier]

Where is the Bohr-Sommerfeld quantization still used?

A lot of useful semiclassical physics is done based on Bohr-Sommerfeld quantization. In particular, modern versions of it are indispensable in the spectroscopy of large molecules, where the more accurate ab initio methods become numerically too demanding.

• Norcliffe, A., & Percival, I. C., Correspondence identities II. The Bohr-Sommerfeld identity for the hydrogen atom. Journal of Physics B: Atomic and Molecular Physics, 1 (1968), 784.
• Colwell, S. M., & Percival, I. C., The semiclassical determination of potential surfaces from observed spectra. I. Chemical Physics, 75 (1983), 215-223.

It is also used for meson spectra in constituent quark models: https://arxiv.org/pdf/hep-ph/0412170
and for the analysis of black holes: https://arxiv.org/pdf/1204.1699
to mention just a few more recent uses.

One more older but interesting survey paper:

• M.V. Berry & K.E. Mount, Semiclassical approximations in wave mechanics. Reports on Progress in Physics, 35 (1972), 315.