Comment on Inverse problem from discrete spectrum in the D = 2 dimensional space (2014 Phys. Scr. 989 085201)

2022 ◽  
Author(s):  
Francisco Marcelo Fernandez
Keyword(s):  
Inverse Problem ◽  
Potential Energy ◽  
Ground State ◽  
Dimensional Space ◽  
Potential Energy Function ◽  
State Density ◽  
Energy Functions ◽  
Sum Rule ◽  
Potential Energy Functions ◽  
Ground State Density

Abstract We analyse a method for the construction of the potential-energy function from the moments of the ground-state density. The sum rule on which some expressions are based appear to be wrong, as well as the moments and potential-energy functions derived for some illustrative examples.

Potential energy functions for the ground state surfaces of SO2 and S2O

1985 ◽  
Vol 56 (4) ◽  
pp. 839-851 ◽  
Author(s):  
J.N. Murrell ◽  
W. Craven ◽  
M. Vincent ◽  
Z.H. Zhu
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Functions ◽  
Potential Energy Functions

Potential energy functions for the ground state X3Σ-and excited state1Σ+of UO

2000 ◽  
Vol 98 (13) ◽  
pp. 875-878 ◽  
Author(s):  
H. Y. Wang ◽  
Z. H. Zhu ◽  
T. Gao ◽  
Y. B. Fu ◽  
X. L. Wang ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Functions ◽  
Potential Energy Functions

Vibrational spectra and analytical potential energy functions of some electronic states of Na2

2017 ◽  
Vol 95 (3) ◽  
pp. 253-261
Author(s):  
Qunchao Fan ◽  
Zhixiang Fan ◽  
Weiguo Sun ◽  
Yi Zhang ◽  
Jia Fu
Keyword(s):  
Potential Energy ◽  
Vibrational Spectra ◽  
Electronic States ◽  
Potential Energy Function ◽  
Spectroscopic Constants ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Analytical Potential ◽  
Consistent Method ◽  
Vibrational Energies

The improved variational algebraic energy consistent method (VAECM) is suggested to study the vibrational spectra and analytical potential energy functions of six excited electronic states [Formula: see text], 21Δg, (5d)1Δg, (6d)1Δg, (7d)1Δg, and (8d)1Δg of Na2. The full vibrational energies, the vibrational spectroscopic constants, the force constants fn, and the expansion coefficients an of the potential are tabulated. The VAECM analytical potential energy function with adjustable parameter λ for each electronic state is determined. The full vibrational energies of each of these electronic states correctly converge to its dissociation energy and have no artificial barrier in all the calculation ranges. The VAECM analytical potentials excellently agree with the Rydberg–Klein–Rees potentials.

The Solution of Axial Symmetry Elastic Plates on a Bossinesq Subgrade with Displacement Variational Principles

2011 ◽  
Vol 90-93 ◽  
pp. 2347-2352
Author(s):  
You Kai Wang ◽  
En Wang ◽  
Wei Min Liang
Keyword(s):  
Potential Energy ◽  
Contact Stress ◽  
Variational Principles ◽  
Potential Energy Function ◽  
Elastic Plates ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Minimum Potential ◽  
External Forces ◽  
Elastic Mechanics

The contact stress between subgrade and subgrade plate was regarded as external force to subgrade. The circular subgrade is divided into rings, and supposing that the contact stress on rings is exerted on elastic subgrade sequentially. The potential energy functions of Bossinesq subgrade are derived by using superposition theorem and Bossinesq solution of elastic mechanics. The potential energy functions were given for the whole system of subgrade, subgrade plate and external forces. The displacement and stress state can be calculated with the principle of minimum potential energy through the potential energy function of the whole system.

Determination of potential energy functions of argon, krypton, and xenon via the inversion of reduced-viscosity collision integrals at zero pressure

2003 ◽  
Vol 81 (7) ◽  
pp. 866-871 ◽  
Author(s):  
Elaheh K Goharshadi ◽  
Mina JamiAlahmadi ◽  
Bijan Najafi
Keyword(s):  
Thermal Conductivity ◽  
Potential Energy ◽  
Pair Potential ◽  
Potential Energy Function ◽  
Collision Integral ◽  
Collision Integrals ◽  
Energy Functions ◽  
Potential Energy Functions ◽  
Reduced Viscosity ◽  
Different Temperatures

The pair potential energy functions of argon, krypton, and xenon have been determined via the inversion of reduced-viscosity collision integrals at zero pressure. A comparison of the potentials with the previously determined potentials are included. The viscosity and thermal conductivity of argon, krypton, and xenon at different temperatures and pressures have been calculated and compared with experimental values. The present potentials for argon, krypton, and xenon provide a good overall account of the experimental properties of these compounds, considering the stated uncertainty in the measurements.Key words: potential energy function, collision integral, viscosity, thermal conductivity.

Regularized vibrational energies prediction and potential energy function study for some interhalogen diatomic molecules

2017 ◽  
Vol 16 (06) ◽  
pp. 1750047 ◽  
Author(s):  
Jia Fu ◽  
Jie Zhan ◽  
Qun Chao Fan ◽  
Hui Dong Li ◽  
Zhi Xiang Fan ◽  
...  
Keyword(s):  
Potential Energy ◽  
Potential Energy Function ◽  
Asymptotic Region ◽  
Validation Dataset ◽  
Energy Functions ◽  
Physical Constraints ◽  
Potential Energy Functions ◽  
Analytical Potential ◽  
Consistent Method ◽  
Vibrational Energies

Full vibrational energies and corresponding analytical potential energy functions (APEFs) for [Formula: see text] of ClF, [Formula: see text] of ICl, [Formula: see text] of IBr, and [Formula: see text]of IF are obtained by four-term variational algebraic energy-consistent method [VAECM(4)]. Three major methods are used to handle the regularization problems and make the results more reliable: (1) physical constraints like progressive dissociation behavior are used to overcome overfitting problems; (2) reasonable variational method is used to expand the experimental dataset and make the model optimization much faster; and (3) validation dataset is used to further enhance the reliability. After these treatments, our results agree well with experiment and have a good physical converged behavior in molecular dissociation and asymptotic region. This study provides important reference data for the related molecules.

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