On the Quantization of the Monoatomic Ideal Gas

This article mainly consists in the quantum mechanical study of an adiabatically compressed particle, in an infinitely high well, which we conjecture, can be considered as the basis of an ideal gas. Thus we prove that, all the compression energy is, as may be expected, transformed into extra kinetic energy of the particle. This result frames a quantum mechanical definition of an ideal gas. It further helps the elucidation of a paradox.

An analytical expression for Fermi-Dirac integrals of arbitrary order is presented,and its applicability in obtaining the EOS of a degenerate,non-relativistic,Fermi gas is discussed.

We find an analytical expression for the specific heat of a Fermi gas in a harmonic trap using a semi-classical approximation. Our approximation is valid for kT>hw and in this range it is shown to be highly accurate. We comment on the semi-classical approximation, presenting an explanation for this high accuracy.

There is a huge number of excellent and comprehensive textbooks on quantum mechanics. They mainly differ for the approach, more or less oriented to the formalism rather than to the phenomenology, as well as for the topics covered. These lectures have been based mainly on the classical textbook by Gasiorowicz (1974). I must confess that the main reason for my choice of Gasiorowicz (1974) is affective, as it was the textbook where I first learned the basic principles of quantum...

The statistical properties of non-interacting bosons and fermions confined in trapping potentials are most easily obtained when the system may exchange energy and particles with a large reservoir (grand-canonical ensemble). There are circumstances, however, where the system under consideration may be considered as being isolated (micro-canonical ensemble). This paper first reviews results relating to micro-canonical ensembles. Some of them were obtained a long time ago, parti...

One-particle properties of non-interacting Fermions in a one-dimensional harmonic trap and at zero temperature are studied. Exact expressions and asymptotic results for large Fermion number N are given for the particle density distribution n_0(z,N). For large N and near the classical boundary at the Fermi energy the density displays increasing fluctuations. A simple scaling of these tails of the density distribution with respect to N is established. The Fourier transform of t...

The ability to directly measure the momentum distribution of quantum gases is both unique to these systems and pivotal in extracting many other important observables. Here we use Raman transitions to measure the momentum distribution of a weakly-interacting Fermi gas in a harmonic trap. For narrow atomic dispersions, momentum and energy conservation imply a linear relation between the two-photon detuning and the atomic momentum. We detect the number of atoms transferred by th...

Once again the possibility of the existence of particle statistics intermediate between those of Fermi-Dirac and Bose-Einstein surfaces. Here attention is drawn to the fact that some fifteen years ago it was shown that such so-called 'intermediate' statistics correspond to no physical process and the stationary probability distributions of intermediate statistics are not compatible with any mechanism which allows a variation between Fermi-Dirac and Bose-Einstein statistics.

In this note we consider three issues related to the unitary Fermi gas in a harmonic trap. We present a short proof of a virial theorem, which states that the average energy of a particle system at unitarity in a harmonic trap is twice larger than the average potential energy. The theorem is valid for all systems with no intrinsic scale, at zero or finite temperature. We discuss the odd-even splitting in a unitarity Fermi gas in a harmonic trap. We show that at large number o...

Exact and closed-form expressions of the particle density, the kinetic energy density, the probability current density, and the momentum distribution are derived for a coherent state of a noninteracting Fermi gas, while such a state can be obtained from the ground state in a $d$-dimensional isotropic harmonic trap by modulating the trap frequency and shifting the trap center. Conservation laws for the relations of the densities are also given. The profile of the momentum dist...