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Springer eBooks

Overview of Momentum Distribution Calculations

J. W. Clark, MANFRED L. RISTIG

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-1-4899-2554-1_2

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The aim is the expected value of helium ions to determine its properties as a heat transmitter to reactors and chirogenic science. This research is non-experimental research using quantum mechanics literature study methods because there are many previous studies that are relevant to this research. Data on the expected value of electron momentum in helium ions is determined based on numerical calculations using the Matlab 2015a program to simplify calculations using ion expectation calculations in momentum. The results obtained are that the electron momentum value in the helium ion can provide an overview of the average momentum value of the helium ion electrons in momentum space. This research data also shows that in momentum space the expected value of electron momentum decreases as the principal quantum number (n) increases. This can be seen when n=1,l =0 then 3p0 = 1.3146, and when n=3,l =0 then 3p0 = 0.5098.
An overview of the Bose–Einstein condensation of correlated atoms in a trap is presented by examining the effect of interparticle correlations to one- and two-body properties of the above systems at zero temperature in the framework of the lowest order cluster expansion. Analytical expressions for the one- and two-body properties of the Bose gas are derived using Jastrow-type correlation function. In addition numerical calculations of the natural orbitals and natural occupation numbers are also carried out. Special effort is devoted for the calculation of various quantum information properties including Shannon entropy, Onicescu informational energy, Kullback–Leibler relative entropy and the recently proposed Jensen–Shannon divergence entropy. The above quantities are calculated for the trapped Bose gases by comparing the correlated and uncorrelated cases as a function of the strength of the short-range correlations. The Gross–Piatevskii equation is solved, giving the density distributions in position and momentum space, which are employed to calculate quantum information properties of the Bose gas.