scholarly journals Minimum-uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators

2021 ◽  
Author(s):  
Marcin Molski
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Coherent States ◽  
Algebraic Approach ◽  
Potential Energy Function ◽  
Exact Analytical Solutions ◽  
Minimum Uncertainty ◽  
Coherent Spectroscopy ◽  
Morse Oscillators ◽  
The Given

AbstractA mixed supersymmetric-algebraic approach is employed to generate the minimum uncertainty coherent states of the hyperbolic and trigonometric Rosen–Morse oscillators. The method proposed produces the superpotentials, ground state eigenfunctions and associated eigenvalues as well as the Schrödinger equation in the factorized form amenable to direct treatment in the algebraic or supersymmetric scheme. In the standard approach the superpotentials are calculated by solution of the Riccati equation for the given form of potential energy function or by differentiation of the ground state eigenfunction. The procedure applied is general and permits derivation the exact analytical solutions and coherent states for the most important model oscillators employed in molecular quantum chemistry, coherent spectroscopy (femtochemistry) and coherent nonlinear optics.

scholarly journals Structure and potential energy function of the ground state of XY(H, Li, Na)

2006 ◽  
Vol 55 (5) ◽  
pp. 2175
Author(s):  
Geng Zhen-Duo ◽  
Fan Xiao-Wei ◽  
Zhang Yan-Song
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Function ◽  
Potential Energy Function

On a Universal Potential Energy Function and the Importance of Ionic Structures for the Ground State of Molecules

1982 ◽  
Vol 37 (9) ◽  
pp. 971-981 ◽  
Author(s):  
G. Van Hooydonk
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Function ◽  
Potential Energy Function ◽  
Covalent Bonding ◽  
Dissociation Energies ◽  
Reasonable Approximation ◽  
Ionic Dissociation ◽  
Vibrational Levels ◽  
Better Than

Abstract The Kratzer-Fues-Varshni-V-potential, applied to ionic dissociation energies, is shown to yield rather accurate potential energy curves in the bonding region for H2, HF, LiH, Li2 and LiF. Vibrational levels, calculated by this ionic approximation to the ground state of widely differing molecules, nearly coincide with RKR-data. At the repulsive side of the curve and up to 2re, the agreement with RKR-curves is even better than for Morse's curve, also for the "covalent" molecules H2 and Li2. Calculated spectroscopical constants αe and ωeχe are far better than those calculated with Morse's function. Even the existence of a maximum in the potential curve at larger r-values seems not in confict with an ionic approximation. From the universal character of the function used, it is concluded that a reasonable approximation for the ground state of all molecules considered is one in terms of ionic structures, even for H2 and especially for Li2. According to the present results, the term “covalent bonding” seems to be definitely superfluous, as the usually made distinction between ionic and covalent bonding is more appearant than real.

scholarly journals Structure and analytic potential energy function for the ground state of SiF2 molecule

2009 ◽  
Vol 58 (8) ◽  
pp. 5280
Author(s):  
Zhao Jun ◽  
Cheng Xin-Lu ◽  
Yang Xiang-Dong ◽  
Zhu Zheng-He
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Function ◽  
Potential Energy Function ◽  
Analytic Potential

scholarly journals Structure and analytic potential energy function for the ground state of SiO2 molecule

2007 ◽  
Vol 56 (1) ◽  
pp. 147
Author(s):  
Wu Dong-Lan ◽  
Cheng Xin-Lu ◽  
Yang Xiang-Dong ◽  
Xie An-Dong ◽  
Yu Xiao-Guang ◽  
...  
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Function ◽  
Potential Energy Function ◽  
Analytic Potential

scholarly journals Structure and potential energy function for the ground state (X2)of TiN molecule

2012 ◽  
Vol 61 (1) ◽  
pp. 013401
Author(s):  
Xiong Xiao-Ling ◽  
Wei Hong-Yuan ◽  
Chen Wen
Keyword(s):  
Potential Energy ◽  
Ground State ◽  
Energy Function ◽  
Potential Energy Function

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.

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