Recent interest in problems in higher space dimensions is becoming increasingly important and attracted the attention of many investigators in variety of fields in physics. In this paper,the electrostatic energy of two geometries (a charged spherical shell and a non-conducting sphere) is calculated in higher space dimension,N. It is shown that as the space dimension increases,up to N = 9, the electrostatic energy of the two geometries decreases and beyond N = 9 it increases. Furthermore, we discuss a simple example which illustrates classical renormalization in electrostatics in higher dimensions.
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
Sami M. Al-Jaber
Some physical properties of the behavior of an ideal non- relativistic Bose gas in N – dimensional space are theoretically investigated. The general analytic expressions of the critical temperature Tc of Bose – Einstein condensation, and the high- temperature behavior of the gas have been derived. The dependence of these physical quantities on space dimension is discussed and some numerical values are calculated. Moreover, the limit of these quantities in the infinite dimensional space (N ) is also examined