If a quantum system is going to transition between two states that have different energy, would we not expect it to take a time specified by the Heisenberg Uncertainty Principle? If the change in energy is delta E, would we not expect the transition to take delta T = h bar/delta E?
> would we not expect it to take a time specified by the Heisenberg Uncertainty Principle?
There isn't actually an energy-time version of the uncertainty principle, at least not the simple one you're assuming here, although many pop science presentations talk as if there is. A good article discussing this is here:
For a quantum system transitioning between states, the probability of transition in general will vary as a function of time; how it varies depends on the specific state of the system. There is no general rule that relates the expected transition time to the change in energy. (Note also that not all transitions are between energy eigenstates.)
No, the time to complete one transition is the inverse of Rabi frequency, which is actually determined by strength of external field and nature of the transition (its dipole moment matrix elements), see e.g. https://en.wikipedia.org/wiki/Rabi_frequency
