The Δk = ±2 "forbidden band" and inversion–rotation energy levels of ammonia

1984 ◽  
Vol 62 (12) ◽  
pp. 1775-1791 ◽  
Author(s):  
Š. Urban ◽  
Romola D'cunha ◽  
K. Narahari Rao ◽  
D. Papoušek
Keyword(s):  
Quantum Number ◽  
State Energy ◽  
Energy Levels ◽  
Data Set ◽  
Quantum Numbers ◽  
Forbidden Transitions ◽  
Fourier Transform Spectra ◽  
The Fourier Transform ◽  
And Inversion ◽  
Rotation Energy

An entire band of perturbation allowed transitions to the ν4 state of 14NH3 has been assigned in the Fourier transform spectra recorded using a 192-m path length. More than 900 of the forbidden transitions provide necessary information on the spacing between the energy levels with different quantum numbers k, inaccessible from allowed transitions. These data were combined with all other relevant data (MW, submillimetrewave, FIR, IR) published in the literature to derive precise values of inversion–rotation energy levels. This extensive data set completely describes the ground state energy levels of 14NH3 up to quantum number J = 16 for all possible values of the quantum number k.

The Δk = ±2 perturbation-allowed ν4 band and inversion-rotation energy levels of 15NH3

1985 ◽  
Vol 111 (2) ◽  
pp. 361-376 ◽  
Author(s):  
Š. Urban ◽  
Romola D'Cunha ◽  
K. Narahari Rao ◽  
D. Papoušek
Keyword(s):  
Energy Levels ◽  
And Inversion ◽  
Rotation Energy

scholarly journals Fisher Information of Free-Electron Landau States

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 268
Author(s):  
Takuya Yamano
Keyword(s):  
Quantum Number ◽  
Fisher Information ◽  
Free Electron ◽  
Principal Quantum Number ◽  
Energy Levels ◽  
Laguerre Polynomials ◽  
Polar Coordinates ◽  
Quantum Numbers ◽  
Lowest Landau Level ◽  
Cylindrical Polar Coordinates

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.

scholarly journals Longpath Fourier Transform Spectra of Ammonia

1987 ◽  
Vol 120 ◽  
pp. 89-90
Author(s):  
R. D'Cunha ◽  
S. Urban ◽  
K. Narahari Rao
Keyword(s):  
Fourier Transform ◽  
Energy Levels ◽  
Complete Information ◽  
Planetary Atmospheres ◽  
Partition Functions ◽  
Laboratory Measurements ◽  
Interstellar Clouds ◽  
Forbidden Transitions ◽  
Fourier Transform Spectra ◽  
Spectral Intensities

The ammonia molecule is known to be useful as a probe for studying conditions inside interstellar clouds and planetary atmospheres. Correct interpretation of interstellar and planetary spectra need to be supported by adequate laboratory measurements. in the present studies we report the high resolution Fourier transform spectra of ammonia recorded with a pathlength of 192m at the Kitt Peak National Observatory. Transitions with intensities that are two orders of magnitude weaker than those that have been reported earlier, have been observed and assigned. These include high J transitions, hot bands and forbidden transitions. These transitions are not saturated under long paths such as those available in planetary atmospheres and are therefore useful in the estimation of temperatures. The forbidden transitions have been processed with other relevant data to provide complete information on the energy levels. Such information is required for the calculation of equilibrium population of energy levels and partition functions, which go into the estimation of spectral intensities and abundances in terrestrial, interstellar and planetary atmospheres.

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 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.

scholarly journals Novel patterns of torsion-inversion-rotation energy levels in the ν11 asymmetric CH-stretch spectrum of methylamine

2013 ◽  
Vol 138 (10) ◽  
pp. 104305 ◽  
Author(s):  
Mahesh B. Dawadi ◽  
C. Michael Lindsay ◽  
Andrei Chirokolava ◽  
David S. Perry ◽  
Li-Hong Xu
Keyword(s):  
Energy Levels ◽  
Rotation Energy

scholarly journals Solution of Q-Deformed D-Dimensional Klein-Gordon Equation Kratzer Potential using Hypergeometric Method

2019 ◽  
Vol 9 (2) ◽  
pp. 163
Author(s):  
Suparmi Suparmi ◽  
Dyah Ayu Dianawati ◽  
Cari Cari
Keyword(s):  
Gordon Equation ◽  
Energy Levels ◽  
Spin Symmetry ◽  
Relativistic Energy ◽  
Dimensional Parameter ◽  
Energy Value ◽  
Quantum Numbers ◽  
Klein Gordon ◽  
Dimensional Parameters ◽  
Klein Gordon Equation

The Q-deformed D-dimensional Klein Gordon equation with Kratzer potential is solved by using Hypergeometric method in the case of exact spin symmetry. The linear radial momentum of D-dimensional Klein Gordon equation is disturbed by the presence of the quadratic radial posisiton. The Klein-Gordon D-dimensional equation is reduced to one-dimensional Schrodinger like equation with variable substitution. The solution of the D-dimensional Klein-Gordon equation is determined in the form of a general equation of the Hypergeometry function using the Kratzer potential variable and the quantum deformation variable. From this equation, relativistic energy and wave function are determined. In addition, the relativistic energy equation can be used to calculate numerical energy levels for diatomic particles (CO, NO, O2) using Matlab R2013a software. The results obtained show that the q-deformed quantum parameters, quantum numbers and dimensions affect the value of relativistic energy for zero-pin particles. The value of energy increases with increasing value of quantum number n, q-deformed parameters, and d-dimensional parameters. Of the three parameters, q-deformed parameter is the most dominant to give change in energy value; the increasing q-deformed parameter causes the energy value increases significantly compared to the d-dimensional parameter and quantum numbers n.

scholarly journals Study of opacity broadening in spectral lines for helium like ions in aluminum plasma which produced by laser

2011 ◽  
Vol 8 (1) ◽  
pp. 54-58
Author(s):  
Baghdad Science Journal
Keyword(s):  
Theoretical Analysis ◽  
Spectral Line ◽  
Quantum Number ◽  
Plasma Density ◽  
Energy Levels ◽  
Spectral Lines ◽  
Aluminum Plasma

A theoretical analysis studied was performed to study the opacity broadening of spectral lines emitted from aluminum plasma produced by Nd-YLF laser. The plasma density was in the range 1028-1026 )) m-3 with length of plasma about ?300) m) , the opacity was studied as function of plasma density & principle quantum number. The results show that the opacity broadening increases as plasma density increases & decreases with the spacing between energy levels of emission spectral line.

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