Calculate the possible values of the energy of a particle of mass m situated inside a deep one-dimensional potential well of width a described by V = 0 for 0 ≤ x ≤ a and V = ∞ elsewhere. An electron is confined within a thin layer of a semiconductor. If the layer can be treated as a deep one-dimensional well, calculate its thickness if the difference in energy between the first and second levels is 0.05eV.