Use of Maximum Entropy to explain the form of Energy States of an Electron in a Potential Well

The base state of an electron in an infinite potential well has the most "space" for the electron state.  Thus it has the maximum entropy. Take that same state and imagine pinching the electrons existence to nil in the middle of the trough.  Now you have state-2.  The electron now exists in a smaller entropic state and guess what?  It contains exploitable energy now. This is like a spring compressed.  The electron can decompress and exert force / expend energy.  For example in an interaction with another atom possibly a recoil could occur.   In a crystal lattice an electron can transfer its energy to the atom next door and in effect yield conduction.  All these are preliminary suppositions subject to more scrutiny. As mentioned before since the electron exists in this potential well in the form of free fall it can not have any acceleration.  Thus its distribution must thoroughly avoid the edges of the well were it would indeed experience accelerations by bouncing and recoiling off of the walls.