Why does total angular momentum cause energy splitting in Lyman Hydrogen series?

  • Context: Graduate 
  • Thread starter Thread starter Goodver
  • Start date Start date
  • Tags Tags
    Hydrogen Splitting
Click For Summary
SUMMARY

The Lyman series of the Hydrogen atom occurs at the n = 2 energy level, influenced by electron orbital coupling. Total angular momentum values of 3/2 and 1/2 arise from this coupling. While the quantum mechanical derivation indicates that energy levels depend solely on the principal quantum number n, the introduction of spin-orbit coupling, a relativistic correction, leads to energy splitting despite the degeneracy of p orbitals. This phenomenon highlights the impact of relativistic effects on atomic structure.

PREREQUISITES
  • Understanding of electron orbital coupling
  • Familiarity with total angular momentum concepts
  • Knowledge of quantum mechanics and energy levels
  • Basic principles of relativistic corrections in quantum systems
NEXT STEPS
  • Study the effects of spin-orbit coupling in atomic physics
  • Learn about relativistic quantum mechanics and its implications
  • Explore the derivation of energy levels in hydrogen-like atoms
  • Investigate the role of degeneracy in quantum systems
USEFUL FOR

Students and professionals in physics, particularly those focusing on quantum mechanics, atomic structure, and relativistic effects in atomic systems.

Goodver
Messages
101
Reaction score
1
I have read that Lyman series of Hydrogen atom occur on the n = 2 level, and it is due to electron orbital coupling.

Suppose I understand what is an electron-orbital coupling, and that one gets 3/2 and 1/2 total angular momentum for n = 2 level.

But, from quantum mechanical derivation of the orbitals of Hydrogen atom, the energy level depends only on n quantum number, and that p orbitals caused by possible set of m numbers are degenerate.

How total angular momentum causes energy splitting, if electron-orbital coupling is due to spin and angular momenta which are degenerate?

Thank you.
 
Physics news on Phys.org
Relativity. The degeneracy is present in the non-relativistic Hamiltonian, where the only potential term is the Coulomb interaction. Spin-orbit coupling comes from a relativistic correction.
 
  • Like
Likes   Reactions: Goodver

Similar threads

Undergrad Photon Emitted without Changing Energy Levels
  • · Replies 8 ·
Replies
8
Views
1K
High School Are electrons in atoms always in eigenstates?
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Does spin orbit coupling cause the split in the energy level of the electron?
  • · Replies 1 ·
Replies
1
Views
3K
Undergrad Why is m_j not a good quantum number in strong-field Zeeman effect?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Does putting a hydrogen atom in a box mix angular momentum states?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Does a free electron have an orbital magnetic moment?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Hydrogen atom: Energies and eigenstates
  • · Replies 17 ·
Replies
17
Views
2K
Undergrad Are certain combinations of quantum numbers (basis vectors) forbidden?
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Exploring the Lamb Shift: G-Factor & Angular Momentum
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Total angular momentum for antiparallel electrons
  • · Replies 22 ·
Replies
22
Views
3K