Effect of Phase Choices in Rovibrational Wavefunctions on the Labeling of K-and l-Type Doubling in Molecular Energy Levels

1983 ◽  
Vol 38 (8) ◽  
pp. 821-834 ◽  
Author(s):  
Koichi Yamada
Keyword(s):  
Matrix Element ◽  
Energy Levels ◽  
Diagonal Matrix ◽  
Phase Factor ◽  
Diagonal Matrix Element ◽  
Phase Dependence ◽  
The Matrix ◽  
Symmetry Species ◽  
Asymmetric Top ◽  
Symmetric Top Molecules

Abstract The change in phase factor of the wavefunction does not affect the absolute value of the matrix element, but does change the phase factor of the off-diagonal matrix element. This phase dependence causes a serious confusion in the sign of some parameters in the molecular Hamiltonian, which appear only in the off-diagonal matrix element; for example, the sign of the l-type doubling constant q of a linear or a symmetric-top molecule. In the present paper, the energy eigenvalues, symmetry species, and labeling of the eigenfunctions are discussed for the K-type doubling of asymmetric-top molecules and for the l-type doubling of linear or symmetric-top molecules in relation to the choices of phases in the basis wavefunctions.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

scholarly journals RECENT RESULTS ON LIGHT HADRON SPECTROSCOPY AT BESIII

2011 ◽  
Vol 02 ◽  
pp. 183-187
Author(s):  
◽  
Y. CHEN
Keyword(s):  
Mass Spectrum ◽  
Matrix Element ◽  
Direct Measurement ◽  
International Workshop ◽  
Charm Physics ◽  
Hadron Spectroscopy ◽  
Threshold Enhancement ◽  
Light Hadron ◽  
The Matrix ◽  
Near Threshold

Several measurements on light hadron spectroscopy have been achieved with Beijing Spectrometry III (BESIII). BESII results such as a near threshold enhancement on the [Formula: see text] invariants mass spectrum namely X(1860) and a resonance X(1835) have been confirmed with 225 million J/ψ data accumulated from June 12, 2009 to July 28, 2009. Along with some other preliminary BESIII results including observations of X(1870), X(2120) and X(2370); the first direct measurement of a0(980)/f0(980) mixing; and an improved measurement on the matrix element of decay η′ → ππη have been reported at the 4th international workshop on charm physics.

scholarly journals The matrix element method at next-to-leading order

2012 ◽  
Vol 2012 (11) ◽  
Author(s):  
John M. Campbell ◽  
Walter T. Giele ◽  
Ciaran Williams
Keyword(s):  
Matrix Element ◽  
Leading Order ◽  
Matrix Element Method ◽  
The Matrix ◽  
Element Method

CASE STUDY OF THE CONVERGENCY OF NONLINEAR PERTURBATION SERIES: MORSE–FESHBACH NONLINEAR SERIES

1999 ◽  
Vol 14 (13) ◽  
pp. 2103-2115 ◽  
Author(s):  
BISWANATH RATH
Keyword(s):  
New York ◽  
Energy Levels ◽  
Perturbation Series ◽  
Nonlinear Perturbation ◽  
Theoretical Physics ◽  
The Matrix ◽  
Diagonalization Method ◽  
Matrix Diagonalization ◽  
Divergent Behavior

We study the divergent behavior of the Morse–Feshbach nonlinear perturbation series (MFNS) [P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Part II (McGraw-Hill, New York, 1953)] for producing convergent energy levels using the ground state of a quartic anharmonic oscillator (AHO) in the strong coupling limit. Numerical calculations have been done up to tenth order. Further comparison of the MFNS convergent result has been made with the matrix diagonalization method.

scholarly journals Isotope analysis of highly enriched “silicon-28” by high-resolution inductively coupled plasma mass spectrometry using an internal standard

2021 ◽  
Vol 25 (2) ◽  
pp. 98-109
Author(s):  
P. A. Otopkova ◽  
◽  
A. M. Potapov ◽  
A. I. Suchkov ◽  
A. D. Bulanov ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Matrix Element ◽  
High Resolution ◽  
Inductively Coupled Plasma ◽  
Internal Standard ◽  
Isotopic Analysis ◽  
Random Component ◽  
Inductively Coupled ◽  
The Matrix ◽  
Plasma Mass Spectrometry

In order to study the isotopic effects in semiconductor materials, single crystals of high chemical and isotopic purity are required. The reliability of the obtained data on the magnitude and the direction of isotopic shifts depends on the accuracy of determining the concentration of all stable isotopes. In the isotopic analysis of enriched “silicon-28” with a high degree of enrichment (> 99.99%), it is necessary to determine the impurities of 29Si and 30Si isotopes at the level of 10-3 ¸ 10-5 at. %. At this concentration level, these isotopes can be considered as impurities. It is difficult to achieve high measurement accuracy with simultaneous registration of the main and “impurity” isotopes in such a wide range of concentrations. The registration of analytical signals of silicon isotopes must be carried out in the solutions with different matrix concentrations. The use of the solutions with the high concentration of the matrix element requires the introduction of corrections for matrix noise and the drift of the instrument sensitivity during the measurement. It is possible to reduce the influence of the irreversible non-spectral interference and sensitivity drift by using the method of internal standardization. The inconsistency of the literature data on the selection criteria for the internal standard required studying the behavior of the signals of the “candidates for the internal standard” for the ELEMENT 2 single-collector high-resolution inductively coupled plasma mass spectrometer on the matrix element concentration and the nature of the solvent, as well as on the solution nebulizing time. Accounting for the irreversible non-spectral matrix noise and instrumental drift in isotopic analysis of enriched “silicon-28” and initial 28SiF4 by inductively coupled plasma mass spectrometry had allowed us to reduce by 3-5 times the random component and by more than an order of magnitude the systematic component of the measurement error in comparison with the external standard method. This made it possible to carry out, with sufficient accuracy, the operational control of the isotopic composition of enriched “silicon-28”, both in the form of silicon tetrafluoride and polycrystalline silicon obtained from it, using a single serial device in the range of isotopic concentrations 0.0001–99.999%.

scholarly journals HILL CIPHER ON SHAMIR’S THREE PASS PROTOCOL

2017 ◽  
Author(s):  
hasdiana
Keyword(s):  
Matrix Element ◽  
Execution Time ◽  
Invertible Matrix ◽  
Multidisciplinary Research ◽  
The Third ◽  
Xor Operation ◽  
Hill Cipher ◽  
The Matrix ◽  
Level Of Difficulty ◽  
Time Required

This preprint has been presented in the 3rd International Conference on Multidisciplinary Research, Medan, october 16 – 18, 2014---In this study the authors use the scheme of Shamir's Three Pass Protocol for Hill Cipher operation. Scheme of Shamir's Three Pass Protocol is an attractive scheme that allows senders and receivers to communicate without the key exchange. Hill Cipher is chosen because of the key-shaped matrix, which is expected to complicate the various techniques of cryptanalyst. The results of this study indicate that the weakness of the scheme of Shamir's Three Pass Protocol for XOR operation is not fully valid if it is used for Hill Cipher operations. Cryptanalyst can utilize only the third ciphertext that invertible. Matrix transpose techniques in the ciphertext aims to difficulties in solving this algorithm. The original ciphertext generated in each process is different from the transmitted ciphertext. The level of difficulty increases due to the use of larger key matrix. The amount of time required for the execution of the program depends on the length of the plaintext and the value of the matrix element. Plaintext has the same length produce different execution time depending on the value of the key elements of the matrix used.

scholarly journals Higher-order Darboux transformations for two-dimensional Dirac systems with diagonal matrix potential

2021 ◽  
Vol 2090 (1) ◽  
pp. 012038
Author(s):  
A Schulze-Halberg
Keyword(s):  
Dirac Equation ◽  
Explicit Form ◽  
Higher Order ◽  
Diagonal Matrix ◽  
Two Dimensional ◽  
Darboux Transformations ◽  
Dirac Systems ◽  
Matrix Potential ◽  
De Vries ◽  
The Matrix

Abstract We construct the explicit form of higher-order Darboux transformations for the two-dimensional Dirac equation with diagonal matrix potential. The matrix potential entries can depend arbitrarily on the two variables. Our construction is based on results for coupled Korteweg-de Vries equations [27].

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