A Confined Hydrogen Atom in A Spherical Cavity in N Dimensions “excited states”

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مصلح, منار عبدالرحيم صالح
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An-Najah National University
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.