I was asked an interesting question once that I'd like to solve but have no idea where to start.
It's hard to remember the exact details but basically:
Two electrons are in a harmonic oscillator potential but in two separate states [itex] \left | m \right \rangle [/itex] and [itex] \left | n \right \rangle [/itex]. I know these are stationary states but the combination of them are not.
I was asked something like what would the energy between the states need to be for the states to oscillate.
My understanding is that this means that the a certain condition electrons have equal probability of transition to the higher state m or dropping to the lower state n so the electrons basically hop back and forth between these states.
Does this make sense and how would I go about approaching this problem with the math?