Hydrogen Transitions/TD Pert Theory

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SUMMARY

This discussion focuses on the discrepancies between two time-dependent perturbation theory solutions for transitions in hydrogen, specifically referencing problem 2 in "solutions5.pdf" and exercise 2.10 in "2s decay.pdf." The key issue lies in the differing equations for the matrix elements, particularly the denominators. Participants are encouraged to identify the underlying reasons for these differences and determine if they are indeed equivalent or if a fundamental misunderstanding exists.

PREREQUISITES
  • Understanding of time-dependent perturbation theory
  • Familiarity with quantum mechanics principles
  • Knowledge of matrix elements in quantum transitions
  • Ability to analyze and compare mathematical equations
NEXT STEPS
  • Review the derivation of time-dependent perturbation theory
  • Examine the specific matrix element equations in both "solutions5.pdf" and "2s decay.pdf"
  • Study the implications of different denominators in quantum mechanics
  • Explore additional resources on quantum transitions and perturbation theory
USEFUL FOR

Students and researchers in quantum mechanics, particularly those studying hydrogen transitions and perturbation theory, will benefit from this discussion.

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Homework Statement


I'm looking at two different time dependent perturbation solutions to transitions in hydrogen, and I'm wondering where the discrepancy comes from.


Homework Equations


See the attached documents- problem 2 in solutions5.pdf and exercise 2.10 in 2s decay.pdf. You'll notice different equations for the matrix elements (specifically the denominators). I'm trying to figure out why these two are different, if they actually are. I'm probably just missing something obvious that makes them equivalent.


The Attempt at a Solution


 

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