- Tuesday, July 1, 2008
- Harmonic Oscillator In An Infinite N- Dimensional Spherical well
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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.