Wavefunction collapse on degenerate states

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SUMMARY

The discussion centers on the wavefunction collapse in quantum mechanics, specifically regarding degenerate energy eigenstates within a Hamiltonian framework, such as that of the hydrogen atom. The participant, Deniz, questions which specific degenerate eigenstate the wavefunction collapses to after an energy measurement and whether the resulting state is a linear combination of these eigenstates. It is established that the new state can indeed be a linear combination of the degenerate eigenstates, with the coefficients determined by the measurement process and the initial state of the system.

PREREQUISITES
  • Understanding of quantum mechanics principles, particularly wavefunction behavior.
  • Familiarity with Hamiltonians and energy eigenstates.
  • Knowledge of angular momentum in quantum systems, especially in hydrogen atoms.
  • Basic grasp of linear algebra concepts related to vector spaces and linear combinations.
NEXT STEPS
  • Study the implications of degenerate states in quantum mechanics.
  • Explore the measurement postulate in quantum mechanics.
  • Learn about the role of coefficients in linear combinations of quantum states.
  • Investigate the concept of superposition and its relation to wavefunction collapse.
USEFUL FOR

Students and enthusiasts of quantum mechanics, physicists exploring quantum state behavior, and anyone interested in the implications of measurements on wavefunctions in degenerate systems.

osturk
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Hello, I am a beginner on the sbject so please correct if I'm using some sloppy terminology. I'll try to be clear.

Consider a Hamiltonian with degenerate energy eigenstates (say the degeneracy is on angular momentum as in hydrogen atom).

Which of the degenerate eigenstates would the wave function collapse on, after an energy measurement?

Would the resulting wave function be a linear combination of the degenerate eigenstates (which has different angular momentum numbers m,l)?
If so, how are the coefficients of the linear combination determined?

Thanks in advance,
Deniz
 
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I guess any of the vectors in the subspace could be the new state, but what do I know ? I don't believe in collapsing anyway.
 

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