Biography
Abstract
We devote a particular attention to the role played by the repulsive interaction in order to determine a various quantities of the Bose gas in a harmonic trap, for example the chemical potential of condensed atoms, the chemical potential of non-condensed atoms, the anomalous fraction and the heat specific capacity at finite temperature as function as the number of atoms. We also calculate their behavior in Thomas Fermi approximation, where the thermal cloud is not negligible. We compare our results with literature and experience, we find a good agreement.
Biography
Abstract
In this paper, Einstein derived ∆L=∆mc2 (light energy –mass equation), it is not completely studied; and is only valid under special conditions of involved parameters, e.g. number of light waves, magnitude of light energy, angles at which waves are emitted and relative velocity v. Einstein considered just two light waves of equal energy, emitted in opposite directions and velocity v is uniform. There are numerous possibilities of parameters which are not considered in Einstein’s derivation. ∆E=∆mc2 is obtained from ∆L=∆mc2 by simply replacing L by E (every energy) without derivation. Fadner pointed out that Einstein neither mentioned E or ∆E=∆mc2, in the derivation which is absolutely correct. Here results are critically analyzed taking all possible variables into account. Under some conditions of valid parameters ∆L=∆mc2 is not obtained, e.g. sometimes result is Ma =Mb or no equation is derivable. If all values of valid parameters are taken into account, then the same derivation also gives L α ∆mc2 or L =A ∆mc2, where A is the coefficient of proportionality. Thus Einstein’s derivation under the valid parameters also predicts that energy emitted may be less or more than ∆L=∆mc2.