Specific heats of degenerate ideal gases

From arguments based on Heisenberg's uncertainty principle and Pauli's exclusion principle, the molar specific heats of degenerate ideal gases at low temperatures are estimated, giving rise to values consistent with the Nerst-Planck Principle (third law of Thermodynamics). The Bose-Einstein condensation phenomenon based on the behavior of specific heat of massive and non-relativistic boson gases is also presented.Comment: 20 pages, in Portuguese, 7 figure

Study of hydrogen atom described by a generalized wave equation: what can we still learn about space dimensionality

Hydrogen atom is supposed to be described by a generalization of Schr\"odinger equation, in which the Hamiltonian depends on an iterated Laplacian and a Coulomb-like potential $r^{-\beta}$. Starting from previously obtained solutions for this equation using the $1/N$ expansion method, it is shown that new light can be shed on the problem of understanding the dimensionality of the world as proposed by Paul Ehrenfest. A surprisingly new result is obtained. Indeed, for the first time, we can understand that not only the sign of energy but also the value of the ground state energy of hydrogen atom is related to the threefold nature of space.Comment: 7 pages, 1 tabl

Applications of the Numerov method to simple quantum systems using Python

Numerov's numerical method is developed in a didactic way by using Python in its {\it Jupyter Notebook} version 6.0.3 for three different quantum physical systems: the hydrogen atom, a molecule governed by the Morse potential and for a quantum dot. After a brief introduction to the Numerov method, the complete code to calculate the eigenfunctions and eigenvalues of the hydrogen atom is presented. The necessary code changes to calculate the other two examples are also provided in the sequel

On the Galilean covariance of the d'Alembert equation for acoustic phenomena

The covariance of the d'Alembert equation for acoustic phenomena -- which is a mechanical wave equation -- under the conventional Galilean transformation is demonstrated without the need to abandon the hypothesis that time is absolute in Classical Mechanics, {what would imply} a modification of Galileo's transformations, as suggested in a paper recently published in this journal.Comment: 4 pages, 1 figur

On the influence of Maxwell--Chern--Simons electrodynamics in nuclear fusion involving electronic and muonic molecules

New results recently obtained (\textit{Annals of Physics} (New York) a.n.~168943) established some non-relativistic ground state solutions for three-body molecules interacting through a Chern--Simons model. Within this model, it was argued that Chern--Simons potential should not help improve the fusion rates by replacing electrons with muons, in the case of particular muonic molecules. This achievement motivated us to investigate quantitatively whether or not the Maxwell--Chern--Simons electrodynamics could influence positively, for example, the probability of having a muon-catalyzed fusion; its contribution to electronic molecules is also considered in this letter. The principal factors related to the probability of elementary nuclear fusion are therefore numerically calculated and compared with their analogs admitting other forms of interaction like $-1/\rho$ and $\ln (\rho)$. The analysis carried on here confirms that one should not expect a significant improvement in nuclear fusion rates in the case of muonic molecules, although, surprisingly, the same is not true for electronic molecules, compared with other theoretical predictions. Numerical predictions for the fusion rates for $ppe$, $pp\mu$, $dde$ and $dd\mu$ molecules are given as well as the predicted value for the tunneling rate for these molecules