An-Najah Staff

We consider the effect of space dimension N, on the results predicted by two approximation techniques applied on physical quantum systems. In the first, we apply degenerate perturbation theory to perturbed N-dimensional infinite cubical well. It is found that the energy difference for splitting decreases as N increases and it vanishes in the infinite dimensional space. In the second, we apply the sudden approximation to the electronic structure change implied by beta-decay of the tritium nucleus. It is found that as N increases the ionization probability increases.

We consider the solution of Schrodinger equation in N dimensions for the infinite N-dimensional spherical potential well. Some aspects of the radial part and the angular part of the wave function are presented and discussed. In particular, the effective potential, orthonormality, energy eigenvalues and the degeneracy are investigated. Thus the role of the topological structure of the configuration space of a physical system on the quantum nature of the system is emphasized.

We compute ground state energies for the N-dimensional hydrogen atom confined in an impenetrable spherical cavity. The obtained results show their dependence on the size of the cavity and the space dimension N. We also examine the value of the critical radius of the cavity in different dimensions. Furthermore, the number of bound states was found for a given radius S, in different space dimensions.