The average energy per fermion in the case of a Fermi gas with any kinematic characteristic, trapped
under the most general power law potential in d -dimension has been calculated at zero temperature.
In a previous paper (Acharyya M 2010 Eur. J Phys. 31 [http://dx.doi.org/10.1088/0143-0807/31/6/L01]
L89 ) it was shown, in the case of a free ideal Fermi gas, as the dimension increases the average
energy approaches the Fermi energy and in infinite dimension the average energy becomes equal to the
Fermi energy at T = 0. In this letter it is shown that, for a trapped system at finite dimension the
average energy depends on a power law exponent, but as the dimension tends to infinity the average
energy coincides with the Fermi energy for any power law exponent. The result obtained in this
manuscript is more general, as we can describe the free system as well as any trapped system with an
appropriate choice of power law exponent, and is true for an…