Sommerfeld quantization condition

Thread starter adiputra
Start date Jan 30, 2010
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In summary, the Sommerfeld quantization condition is a rule in quantum mechanics developed by Arnold Sommerfeld that determines the allowed energy levels for a bound system. It differs from Bohr's model by considering elliptical orbits and the angular momentum of the system, resulting in a more accurate prediction of spectral lines. This condition is significant for providing a mathematical framework and explaining fine structure in spectral lines, but has limitations in its applicability to systems with a central force and its inability to account for relativistic effects.

Jan 30, 2010

adiputra

1. The allowable radius of spinning electron in uniform magnetic field using sommerfield quantization condition

3. Subs mv/r=qvB and some of its variation (like th period 2pi*r /v) into the closed int of pdq=nh and I got r=sqr((nh)/(2pi*qB)). Is this correct. I can't find anything about this equation in the internet.

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Feb 3, 2010

thebigstar25

what is your question exactly?

What is the Sommerfeld quantization condition?

The Sommerfeld quantization condition is a rule in quantum mechanics that determines the allowed energy levels for a bound system, such as an electron orbiting an atom. It states that the angular momentum of the system must be an integer multiple of Planck's constant divided by 2π.

Who developed the Sommerfeld quantization condition?

The Sommerfeld quantization condition was developed by the German physicist Arnold Sommerfeld in the early 20th century. He used it to extend Niels Bohr's model of the atom by including elliptical orbits and explaining the fine structure of spectral lines.

How does the Sommerfeld quantization condition differ from Bohr's model?

Bohr's model of the atom only allowed for circular orbits with discrete energy levels, while the Sommerfeld quantization condition allows for elliptical orbits and considers the angular momentum of the system. This results in a more accurate prediction of observed spectral lines.

What is the significance of the Sommerfeld quantization condition?

The Sommerfeld quantization condition is significant because it provides a mathematical framework for understanding the quantization of energy levels in bound systems. It also helps to explain the fine structure of spectral lines and has applications in fields such as atomic and molecular physics.

Are there any limitations to the Sommerfeld quantization condition?

Yes, the Sommerfeld quantization condition is limited to systems with a central force, such as the Coulomb force between an electron and a nucleus. It also does not take into account relativistic effects, which become significant for high atomic numbers or high energies.