scholarly journals Numerical Calculation of Energy Eigen-values of the Hydrogen Negative Ion in the 2p^2 Configuration by Using the Variational Method

2020 ◽  
Vol 24 (1) ◽  
pp. 30
Author(s):  
Yosef Robertus Utomo ◽  
Guntur Maruto ◽  
Agung Bambang Setio Utomo ◽  
Pekik Nurwantoro ◽  
Sholihun Sholihun
Keyword(s):  
Numerical Calculation ◽  
Variational Method ◽  
Trial Function ◽  
Hydrogen Molecule ◽  
Negative Ion ◽  
Multipole Moments ◽  
A Value ◽  
Eigen Value ◽  
Eigen Values ◽  
Electric Multipole Moments

Calculation of energy eigen value of hydrogen negative ion (H − ) in 2p^2 configuration using the method of variation functions has been done. A work on H − can lead to calculations of electric multipole moments of a hydrogen molecule. The trial function is a linear combination of 8 expansion terms each of which is related to the Chandrasekhar’s basis. This work produces a series of 7 energy eigen values which converges to a value of −0.2468 whereas the value of this convergence is expected to be −0.2523. This deviation from the expected value is mainly due to the elimination of interelectronic distance (u) coordinate. The values of the exponent parameters used in this work contribute also to this deviation. This variational method will be applied to the construction of some energy eigen functions of Hv2 .

Identification of kinematic chains and distinct mechanisms using extended adjacency matrix

2007 ◽  
Vol 221 (1) ◽  
pp. 81-88 ◽  
Author(s):  
A Mohammad ◽  
R A Khan ◽  
V P Agrawal
Keyword(s):  
Adjacency Matrix ◽  
Kinematic Chain ◽  
Theoretic Approach ◽  
Kinematic Chains ◽  
Graph Theoretic ◽  
The Past ◽  
Graph Theoretic Approach ◽  
The Family ◽  
Eigen Value ◽  
Eigen Values

Development of the methods for generating distinct mechanisms derived from a given family of kinematic chains has been persued by a number of researchers in the past, as the distinct kinematic structures provide distinct performance characteristics. A new method is proposed to identify the distinct mechanisms derived from a given kinematic chain in this paper. Kinematic chains and their derived mechanisms are represented in the form of an extended adjacency matrix [EA] using the graph theoretic approach. Two structural invariants derived from the eigen spectrum of the [EA] matrix are the sum of absolute eigen values EA∑ and maximum absolute eigen value EAmax. These invariants are used as the composite identification number of a kinematic chain and mechanism and are tested to identify the all-distinct mechanisms derived from the family of 1-F kinematic chains up to 10 links. The identification of distinct kinematic chains and their mechanisms is necessary to select the best possible mechanism for the specified task at the conceptual stage of design.

Calculation of molecular electric multipole moments

1985 ◽  
Vol 25 (6) ◽  
pp. 951-953 ◽  
Author(s):  
I. I. Guseinov ◽  
T. M. Mursalov ◽  
V. T. Aliev
Keyword(s):  
Multipole Moments ◽  
Electric Multipole Moments

Eigen function and corresponding eigen values of charge carriers in V-grooves quantum wires with variable width

2016 ◽  
Vol 30 (17) ◽  
pp. 1650103
Author(s):  
Ali Hossein Mohammad Zaheri
Keyword(s):  
Effective Potential ◽  
Quantum Wire ◽  
Quantum Wires ◽  
Wave Functions ◽  
Charge Carriers ◽  
Energy Spectra ◽  
Eigen Value ◽  
Eigen Values ◽  
Interface Geometry ◽  
Good Agreement

In this work, we have calculated analytically the energy spectra of electrons and holes in V-grooves quantum wires. To modify wire structure, we have used the equations which suggested in the work of Inoshita et al. We introduce a new effective potential scheme which is applicable and matchable with actual interface geometry of this groove of ridge quantum wires. By applying this effective potential and considering a suitable transformed coordinate that allows the decoupling of the two-dimensional wave functions, we have calculated eigen values of the charge carriers in three states as well as the wave functions. We found that by increasing the curvature at the top of quantum wire [Formula: see text] the energy eigen value decreases. Our results are in good agreement with the earlier investigations.

scholarly journals Rayleigh-Bѐnard Convection in a Second-Order Fluid with Maxwell-Cattaneo Law

2012 ◽  
Vol 2 ◽  
pp. 24-32 ◽  
Author(s):  
Smita Saklesh Nagouda ◽  
Subbarama Pranesh
Keyword(s):  
Boundary Conditions ◽  
Critical Rayleigh Number ◽  
Propagation Speed ◽  
Heat Propagation ◽  
Second Order ◽  
Onset Of Convection ◽  
Eigen Value ◽  
Eigen Values ◽  
Heat Flux Law ◽  
Short Times

The objective of the paper is to study the Rayleigh-Bѐnard convection in second order fluid by replacing the classical Fourier heat law by non-classical Maxwell-Cattaneo law using Galerkin technique. The eigen value of the problem is obtained using the general boundary conditions on velocity and third type of boundary conditions on temperature. A linear stability analysis is performed. The influence of various parameters on the onset of convection has been analyzed. The classical Fourier flux law over predicts the critical Rayleigh number compared to that predicted by the non-classical law. The present non-classical Maxwell-Cattaneo heat flux law involves a wave type heat transport (SECOND SOUND) and does not suffer from the physically unacceptable drawback of infinite heat propagation speed. It is found that the results are noteworthy at short times and the critical eigen values are less than the classical ones. Over stability is the preferred mode of convection.

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