A confined 3Thydrogen atom3T in higher space dimensions

The Schrödinger equation for the confined H-atom in N dimensional spherical cavity has been solved. It has been shown that the wave functions are dimension-dependent and having the same form as those of the free hydrogen atom in N- dimensions.The ground state energies for the confined hydrogen atom in N dimensional impenetrable spherical cavity have been computed.The obtained results show their dependence on the size of the cavity and the space dimension N.

The pressure exerted on the wall of the cavity due to enclosing the H-atom inside a cavity of radius S was discussed.

We found that the pressure depends on N and S, and for a given N, the pressure increases with decreasing the radius of the cavity up to a maximum value Pmax and then starts to decrease. The value of this Pmax increases with increasing N, and the value of the radius of the cavity at which the pressure is maximum increases as N increases also.