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6.2: Notes

( \newcommand{\kernel}{\mathrm{null}\,}\)

  • The ‘Matrix element’ V21 determines whether there is a transition from an initial state 1 to a final state 2 even if ˆV is independent of time. It also determines the rate of the transition.
  • If the states |1 and |2 are eigenstates of the perturbation ˆV then V21=V12=0 and no transition occurs.
  • Over a long period of time, the system will oscillate between the two states.
  • Perturbation theory, in essence, ignores the third-order possibility of ending up in state 2 via |1|2|1|2
  • The mathematics is the same as for two coupled pendula, where the energy moves back and forth between the two bobs.
  • The states can represent anything, and oscillation will occur whenever there are off diagonal terms in the matrix.
  • Examples: (see Feynman III Ch.9-11) Nitrogen atom in ammonia, electron in H+2, pion exchange, benzene, electron spins, photon polarization, neutrino oscillations, neutral kaons.

This page titled 6.2: Notes is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Graeme Ackland via source content that was edited to the style and standards of the LibreTexts platform.

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