A Perturbation Theory for the Population of Atomic Energy Levels in Non-Lte Plasmas

1988 ◽  
Vol 102 ◽  
pp. 343-347
Author(s):  
M. Klapisch
Keyword(s):  
Perturbation Theory ◽  
Small Parameter ◽  
Classification Scheme ◽  
Sum Rules ◽  
Energy Levels ◽  
Natural Classification ◽  
Quantum Numbers ◽  
Formal Expansion ◽  
Atomic Energy Levels ◽  
As Effects

AbstractA formal expansion of the CRM in powers of a small parameter is presented. The terms of the expansion are products of matrices. Inverses are interpreted as effects of cascades.It will be shown that this allows for the separation of the different contributions to the populations, thus providing a natural classification scheme for processes involving atoms in plasmas. Sum rules can be formulated, allowing the population of the levels, in some simple cases, to be related in a transparent way to the quantum numbers.

scholarly journals Penggunaan Teori Perturbasi untuk Menentukan Tingkat Energi Partikel pada Kotak Potensial Tiga Dimensi

2020 ◽  
Vol 6 (2) ◽  
Author(s):  
Indah Kharismawati
Keyword(s):  
Perturbation Theory ◽  
Energy Level ◽  
Electric Fields ◽  
Magnetic Energy ◽  
Energy Levels ◽  
Particle Energy ◽  
The Core ◽  
Quantum Numbers ◽  
Energy Disorder ◽  
Number Of Particles

<p><em>Hamiltonian a known system in many matters does not guarantee that the equation can be resolved, e.g. due to minor disturbances such as electric fields or magnetic fields that can lead to slight changes in energy and its particle functions, for such issues it should be used disorder theory (perturbation theory). The perturbation theory can determine how much the result of the presence of disruption to energy levels and Eigen's functions. The energy possessed by particles in addition to being influenced by quantum numbers (n<sub>x</sub>, n<sub>y</sub> and n<sub>z</sub>) and the size of the potential box are also influenced by interference in the form of magnetic energy produced due to the motion of particles (electrons) in the core intrinsic magnetic field (proton) which affects the energy value does not appear due to the value of this magnetic energy disorder is very small, while for interference that is an extrinsic magnetic energy has shown a 10 (Tesla). The wider the size of the box then the energy that the particles have is smaller so that the energy level and the particle energy spectrum in the potential box will appear continuous. It can be concluded that the particle energy level relies on the length of the potential box, the quantum number of particles, and also the interference that particles have.   </em></p>

scholarly journals Semiclassical calculations of the quadruple excited four-electron systems

2007 ◽  
pp. 33-44
Author(s):  
N. Simonovic ◽  
M. Predojevic ◽  
V. Pankovic ◽  
P. Grujic
Keyword(s):  
Energy Levels ◽  
Point Of View ◽  
Interstellar Space ◽  
Vibrational Modes ◽  
Electron Systems ◽  
Atomic Systems ◽  
Excited Atoms ◽  
Relative Contribution ◽  
Quantum Numbers ◽  
Semiclassical States

Highly excited atoms acquire very large dimensions and can be present only in a very rarified gas medium, such as the interstellar space. Multiply excited beryllium-like systems, when excited to large principal quantum numbers, have a radius of r ? 10 ?. We examine the semiclassical spectrum of quadruple highly excited four-electron atomic systems for the plane model of equivalent electrons. The energy of the system consists of rotational and vibrational modes within the almost circular orbit approximation, as used in a previous calculation for the triply excited three-electron systems. Here we present numerical results for the beryllium atom. The lifetimes of the semiclassical states are estimated via the corresponding Lyapunov exponents. The vibrational modes relative contribution to the energy levels rises with the degree of the Coulombic excitation. The relevance of the results is discussed both from the observational and heuristic point of view.

On Bose-Einstein Condensation

1954 ◽  
Vol 50 (1) ◽  
pp. 65-76 ◽  
Author(s):  
P. T. Landsberg
Keyword(s):  
Closed System ◽  
Canonical Ensemble ◽  
Energy Levels ◽  
Volume Density ◽  
Einstein Condensation ◽  
Bose Einstein Condensation ◽  
Quantum Numbers ◽  
Finite Integer ◽  
Bose Einstein ◽  
Grand Canonical

ABSTRACTThis paper contains a proof that the description of the phenomenon of Bose-Einstein condensation is the same whether (1) an open system is contemplated and treated on the basis of the grand canonical ensemble, or (2) a closed system is contemplated and treated on the basis of the canonical ensemble without recourse to the method of steepest descents, or (3) a closed system is contemplated and treated on the basis of the canonical ensemble using the method of steepest descents. Contrary to what is usually believed, it is shown that the crucial factor governing the incidence of the condensation phenomenon of a system (open or closed) having an infinity of energy levels is the density of states N(E) ∝ En for high quantum numbers, a condition for condensation being n > 0. These results are obtained on the basis of the following assumptions: (i) For large volumes V (a) all energy levels behave like V−θ, and (b) there exists a finite integer M such that it is justifiable to put for the jth energy level Ej= c V−θand to use the continuous spectrum approximation, whenever j ≥ M c θ τ are positive constants, (ii) All results are evaluated in the limit in which the volume of the gas is allowed to tend to infinity, keeping the volume density of particles a finite and non-zero constant. The present paper also serves to coordinate much of previously published work, and corrects a current misconception regarding the method of steepest descents.

Calculation of vibrational HDO energy levels: Analysis of perturbation theory series

2013 ◽  
Vol 114 (3) ◽  
pp. 359-367 ◽  
Author(s):  
A. D. Bykov ◽  
K. V. Kalinin ◽  
A. N. Duchko
Keyword(s):  
Perturbation Theory ◽  
Energy Levels ◽  
Theory Series
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