Energy eigenvalues and Einstein coefficients for the one-dimensional confined harmonic oscillators

We compute the energy eigenvalues and the Einstein coefficients for a one-dimensional harmonic oscillator confined in a box of impenetrable walls as a function of box size, and an asymmetry parameter. The energy eigenvalues that we obtain for, the symmetric and unsymmetric confinement are more accurate than those reported previously. To compute eigenvalues and eigenfunctions we use two different approaches known to be very accurate. With respect to the unbounded harmonic oscillator we find transitions that are now allowed due to the confinement to the box. When the confinement is asymmetric the transition spectra become more complex, since the transition probabilities show a strong variation with box size.