Harmonic oscillator in an infinite N. dimensional sperical well

Abstract EN

The boundary effects on a quantum system are discussed by examining an N- dimensional harmonic oscillator confined in an impenetrable spherical well.

The corrections, due to the boundary and the space dimension, to the ground- state energy and wave function are calculated by using a linear approximation method which is linear in energy and by numerical method using Mathematica.

Our results for the energy corrections obtained by the two methods are in very good agreement.

A simple analytical expression for the asymptotic dependence of the ground - state energy on the well radius and on the dimension N is derived.

Finally, the pressure needed to compress a free N-dimensional harmonic oscillator to a certain size is computed.