Comment on: “An Operator Domain Paradox and the Relativistic Correction to Energy Levels”

1973 ◽  
Vol 41 (9) ◽  
pp. 1119-1120
Author(s):  
M. G. Calkin
Keyword(s):  
Energy Levels ◽  
Relativistic Correction ◽  
Operator Domain

ELECTRONIC PROPERTIES OF A HYDROGENIC IMPURITY IN A QUANTUM WIRE WITH V-SHAPED CROSS-SECTION: SPIN-ORBIT COUPLING, RELATIVISTIC CORRECTION AND CONDUCTANCE

2013 ◽  
Vol 24 (07) ◽  
pp. 1350041 ◽  
Author(s):  
R. KHORDAD ◽  
H. BAHRAMIYAN
Keyword(s):  
Cross Section ◽  
Quantum Wire ◽  
Energy Levels ◽  
Relativistic Correction ◽  
Orbit Coupling ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Hydrogenic Impurity ◽  
Mass Approximation ◽  
Shaped Cross Section

The effects of spin-orbit coupling (SOC) and relativistic correction (RC) on the energy levels of a hydrogenic impurity in a GaAs/Ga 1-x Al x As quantum wire are studied. The quantum wire has a V-shaped cross-section and the impurity located in its center. Our numerical calculations have done using a variational procedure within the effective mass approximation. Our results show that (i) the splitting due to the SOC decreases with increasing the wire width, (ii) the SOC and RC increase when the concentration increases, (iii) the SOC is zero for l = 0 (l is angular momentum) and nonzero for l ≠ 0, (iv) for a given wire width, the RC is different for l = 0 and l = 1 due to expectation values of [Formula: see text] and [Formula: see text] (r is distance between the electron and impurity). We also computed the conductance of the quantum wire with and without impurity.

scholarly journals Energy levels in muonic helium

2019 ◽  
Vol 222 ◽  
pp. 03009
Author(s):  
A.V. Eskin ◽  
V.I. Korobov ◽  
A.P. Martynenko ◽  
V.V. Sorokin
Keyword(s):  
Hyperfine Structure ◽  
Bound States ◽  
Energy Levels ◽  
Computer Code ◽  
Bound State ◽  
Relativistic Correction ◽  
Matrix Elements ◽  
Gaussian Form ◽  
Stochastic Variational Method ◽  
The Matrix

The energy spectrum of bound states and hyperfine structure of muonic helium is calculated on the basis of stochastic variational method. The basis wave functions of muonic helium are taken in the Gaussian form. The matrix elements of the Hamiltonian are calculated analytically. For numerical calculation a computer code is written in the MATLAB system. As a result, numerical values of bound state energies and hyperfine structure are obtained. We calculate also correction to the structure of the nucleus, vacuum polarization and relativistic correction.

scholarly journals Semiclassical perturbation Stark shifts of singly charged argon spectral lines

2019 ◽  
Vol 488 (2) ◽  
pp. 2473-2479
Author(s):  
Rafik Hamdi ◽  
Nabil Ben Nessib ◽  
Sylvie Sahal-Bréchot ◽  
Milan S Dimitrijević
Keyword(s):  
Energy Levels ◽  
Relativistic Correction ◽  
Spectral Lines ◽  
Oscillator Strengths ◽  
Perturbation Approach ◽  
Hartree Fock ◽  
Calculated Energy ◽  
Impact Approximation ◽  
Singly Charged ◽  
Experimental Values

AbstractUsing semiclassical perturbation approach in impact approximation, Stark shifts for singly charged argon (Ar ii) spectral lines have been calculated. Energy levels and oscillator strengths needed for this calculation were determined using Hartree–Fock method with relativistic correction (HFR). We compare our results with experimental values for 100 spectral lines. We also present results as a function of temperature for 161 spectral lines for collisions with electrons, protons, singly charged helium and singly charged argon. This work extends our previous one.

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.

Low-lying energy levels of the FeH molecule

1999 ◽  
Vol 97 (1) ◽  
pp. 93-103 ◽  
Author(s):  
DANIEL F. HULLAH, RICHARD F. BARROW, JOHN
Keyword(s):  
Energy Levels

Do Atomic Spectra Determine Energy Levels?

1995 ◽  
Vol 5 (8) ◽  
pp. 949-961 ◽  
Author(s):  
C. Billionnet
Keyword(s):  
Energy Levels ◽  
Atomic Spectra
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