Squeezed states of electrons and transitions of the density of states

Electron systems which have low dimensional properties have been constructed by squeezing the motion in zero, one, or two-directions. An isolated quantum dot is modeled by a potential box with delta-profiled, penetrable potential walls embedded in a large outer box with infinitely high potential walls which represent the world function with respect to vacuum. We show the smooth crossover of the density of states from the three-dimensional to the quasi-zero dimensional electron gas.