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.