Is the Hydrogen Energy Level Formula Truly Degenerate in j?

In summary, the fine structure of hydrogen refers to the subtle energy differences between different energy levels of the hydrogen atom, caused by the electron's spin and orbital angular momentum and relativistic effects. It is important in various fields and is calculated using classical and quantum mechanics, taking into account relativistic effects. The fine structure constant is a fundamental constant in the study of hydrogen and can be observed using spectroscopy.
  • #1
copernicus1
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Griffiths writes that the formula for the hydrogen energy levels taking fine structure into account "breaks the degeneracy in [itex]l[/itex]" but "still preserves degeneracy in [itex]j[/itex]." I'm confused by this, because the formula he gives (Eq. 6.67 in the textbook) depends on [itex]j[/itex]. How can the system be degenerate in [itex]j[/itex] if the energies depend on [itex]j[/itex]?
 
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  • #2
"The system is degenerate in j" = "different states with the same j have the same energy"
States with different j can have a different energy, even with the same l.
 

Related to Is the Hydrogen Energy Level Formula Truly Degenerate in j?

1. What is the fine structure of hydrogen?

The fine structure of hydrogen refers to the subtle energy differences between different energy levels of the hydrogen atom. These energy differences are caused by the spin and orbital angular momentum of the electron, as well as relativistic effects.

2. Why is the fine structure of hydrogen important?

The fine structure of hydrogen has important implications in fields such as atomic physics, quantum mechanics, and astrophysics. It helps us better understand the behavior and properties of atoms, and can also be used to measure the values of fundamental physical constants.

3. How is the fine structure of hydrogen calculated?

The fine structure of hydrogen is calculated using a combination of classical and quantum mechanics. This involves solving the Schrödinger equation and taking into account relativistic effects, such as the spin-orbit coupling and the Thomas precession.

4. What is the significance of the fine structure constant in hydrogen?

The fine structure constant, also known as alpha, is a dimensionless constant that describes the strength of the electromagnetic interaction between particles. It is a fundamental constant in the study of hydrogen and plays a crucial role in determining the fine structure of the atom.

5. Can the fine structure of hydrogen be observed?

Yes, the fine structure of hydrogen can be observed through spectroscopic techniques. By analyzing the different frequencies of light emitted or absorbed by the atom, scientists can measure the energy differences between the fine structure levels and confirm the existence of the fine structure of hydrogen.

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