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We compute the energy eigenvalues for the N -dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N . The obtained results are compared with those for the free N -dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.

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.

A derivation of the specific electrostatic energy loss for two interacting capacitors is given. The connecting wires are assumed to be superconducting. The method of derivation is based purely on the Poynting vector involved in the process without any reference to the nature of the mechanism that may be involved in achieving a final equilibrium state.

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