Quantum confinement

Quantum confinement restricts a particle's wavefunction over a length comparable with its characteristic quantum length scales, altering the allowed energy levels relative to a bulk material. For a parabolic band confined over width $L$, a characteristic spacing is of order ${\hslash }^2/(m^{\ast }{L}^2)$, with boundary-dependent numerical factors. A quantum dot confines all three directions; confinement in only one direction can leave continuous motion in the other two. Finite barrier height and interactions modify the simplest infinite-wall estimates.