A Confined Hydrogen Atom in A Spherical Cavity in N Dimensions “excited states”
Date
2017-04-06
Authors
مصلح, منار عبدالرحيم صالح
Journal Title
Journal ISSN
Volume Title
Publisher
An-Najah National University
Abstract
The energy eigenvalues for the excited states of a confined Hydrogen atom in an impenetrable spherical cavity in N-dimensional space had been calculated by applying the boundary conditions to the radial wave function of this quantum problem which had been investigated by Shaqqur and AL-Jaber [1].
The energy eigenvalues for the excited states depend on both the space dimension and the cavity size. So, we had investigated the dependence of these energies on the dimension N and on the radius of the cavity S. Also, we deduced the limits of the cavity size at which the H-atom still has bound states. For certain N, when the cavity radius increases enough the H-atom become free atom while when it decreases enough there will be no bound states beyond; these critical values of the cavity radius had been obtained for different dimensions N.
Moreover, we had derived a simple equation which shows the relation between higher excited states with respect to higher dimensions started from N=3.
Finally, we had examined the behavior of the pressure exerted by the confined H-atom on the cavity as the radius S is varied in different space dimensions. We found that: for a fixed N, the pressure gradually increases as the cavity radius decreases up to a maximum value, suddenly after it, the value of pressure diminishes to zero.