Recently started to learn how the confinement in quantum dots affects the momentum and position of the electron wave as the dot gets smaller. As possible positions of the wave become smaller, the uncertainty of the momentum becomes bigger.
Yet, the increase in momentum seems like it would violate conservation of energy to me.
Imagine the following thought experiment. There is an electron looping around an electric field at constant velocity. As it moves, it will release cyclotron radiation corresponding to its mass and velocity.
Now say we envelop it in a spherical donut that keeps progressively shrinking. As its position becomes more known, its momentum will change, being either a big numerical answer or smaller. Simultaneously, as it has a constant velocity; the only way for its momentum to change is by an increase in mass, i.e its velocity should not be relativistic.
As it revolves and its mass oscillates, it will release very high energy/frequency radiation when its momentum becomes high and low frequency/energy radiation when the mass is low. Wouldn’t this be breaking conservation of energy? It would taking energy out of apparent nothingness when as it emits higher energy that when it has lower mass at a random moment in time.
Unless my thought experiment or my conceptual understanding is erroneous, how would this not break conservation of energy?
