Einstein coefficients and dipole moments for the asymmetrically confined harmonic oscillator

We study confinement effects on the energy eigenvalues, dipole moments and Einstein coefficients of a model harmonic oscillator restricted by two impenetrable walls placed either symmetrically or asymmetrically with respect to the potential minimum. The calculations are made using perturbation theory as a function of the position of the potential minimum with respect to the bounding walls. For small boxes, the energy levels resemble more closely those of a free particle in a box, than those of an unbounded harmonic oscillator. When the size of the box increases, the lowest energy levels become more similar to those of the unbounded harmonic oscillator, but the highest energy levels remain similar to those of the free particle in a box. We also show that the selection rules for the confined harmonic oscillator are not the same as those of the unbounded harmonic oscillator.