To take an example,
Let's think of an electron which ban be in either one of two positions [...] There are two possible states of definite energy for the electron. Each state can be described by the amplitude for the electron to be in each of the two basic positions. In either of the definite-energy states, the magnitudes of these two amplitudes are constant in time, and the phases vary in time with the same frequency. On the other hand, if we start the electron in one position, it will later have moved to the other, and still later will swing back to the first position.
(Feynman derives this behaviour from first principles in chapter 8-6 by solving equations for the state of an ammonia molecule, but that's a nice summary).
This sounds like the uncertainty principle - that you can know energy or position but not both. Is it possible to derive the uncertainty principle from such an analysis? Or is the uncertainty principle somehow axiomatic in the way this behaviour is derived?