Prospect of Retrieving Vibrational Wave Function by Single-Object Scattering Sampling

2013 ◽  
Vol 4 (19) ◽  
pp. 3345-3350 ◽  
Author(s):  
Hosung Ki ◽  
Kyung Hwan Kim ◽  
Jeongho Kim ◽  
Jae Hyuk Lee ◽  
Joonghan Kim ◽  
...  
Keyword(s):  
Wave Function ◽  
Single Object ◽  
Vibrational Wave Function ◽  
Object Scattering

Calculation of the vibrational wave function of polyatomic molecules

2000 ◽  
Vol 112 (6) ◽  
pp. 2655-2667 ◽  
Author(s):  
Per-Olof Åstrand ◽  
Kenneth Ruud ◽  
Peter R. Taylor
Keyword(s):  
Wave Function ◽  
Polyatomic Molecules ◽  
Vibrational Wave Function

scholarly journals Spatial Imaging of theH2+Vibrational Wave Function at the Quantum Limit

2012 ◽  
Vol 108 (7) ◽  
Author(s):  
L. Ph. H. Schmidt ◽  
T. Jahnke ◽  
A. Czasch ◽  
M. Schöffler ◽  
H. Schmidt-Böcking ◽  
...  
Keyword(s):  
Wave Function ◽  
Quantum Limit ◽  
Vibrational Wave Function

scholarly journals Novel Single-Molecule Technique by Single-Object Scattering Sampling (SOSS)

2011 ◽  
Vol 32 (6) ◽  
pp. 1849-1850 ◽  
Author(s):  
Hyotcherl Ihee
Keyword(s):  
Single Molecule ◽  
Single Object ◽  
Object Scattering

Other Applications of Neural Networks to Quantum Mechanical Problems

2012 ◽  
Author(s):  
Lionel Raff ◽  
Ranga Komanduri ◽  
Martin Hagan ◽  
Satish Bukkapatnam
Keyword(s):  
Neural Networks ◽  
Wave Function ◽  
Linear Combination ◽  
Vibrational Spectra ◽  
Schrodinger Equation ◽  
Usual Method ◽  
Basis Functions ◽  
Wave Functions ◽  
Quantum Mechanical ◽  
Vibrational Wave Function

The usual method for solving the vibrational Schrödinger equation to obtain molecular vibrational spectra and the associated wave functions generally involves the expansion of the vibrational wave function, ψk(y), in terms of a linear combination of a set of basis functions.

scholarly journals Solution of the Rovibrational Schrödinger Equation of a Molecule Using the Volterra Integral Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Mahmoud Korek ◽  
Nayla El-Kork
Keyword(s):  
Integral Equation ◽  
Wave Function ◽  
Volterra Integral Equation ◽  
Vibrational Energy ◽  
Excited Electronic State ◽  
Rotational Constant ◽  
Vibrational Wave Function ◽  
Oppenheimer Approximation ◽  
Centrifugal Distortion Constants ◽  
Schrödinger Perturbation

By using the Rayleigh-Schrödinger perturbation theory the rovibrational wave function is expanded in terms of the series of functions ϕ0,ϕ1,ϕ2,…ϕn, where ϕ0 is the pure vibrational wave function and ϕι are the rotational harmonics. By replacing the Schrödinger differential equation by the Volterra integral equation the two canonical functions α0 and β0 are well defined for a given potential function. These functions allow the determination of (i) the values of the functions ϕι at any points; (ii) the eigenvalues of the eigenvalue equations of the functions ϕ0,ϕ1,ϕ2,…ϕn which are, respectively, the vibrational energy Ev, the rotational constant Bv, and the large order centrifugal distortion constants Dv,Hv,Lv….. Based on these canonical functions and in the Born-Oppenheimer approximation these constants can be obtained with accurate estimates for the low and high excited electronic state and for any values of the vibrational and rotational quantum numbers v and J even near dissociation. As application, the calculations have been done for the potential energy curves: Morse, Lenard Jones, Reidberg-Klein-Rees (RKR), ab initio, Simon-Parr-Finlin, Kratzer, and Dunhum with a variable step for the empirical potentials. A program is available for these calculations free of charge with the corresponding author.

scholarly journals Influence of retardation on the vibrational wave function and binding energy of the helium dimer

1993 ◽  
Vol 98 (12) ◽  
pp. 9687-9690 ◽  
Author(s):  
Fei Luo ◽  
Geunsik Kim ◽  
George C. McBane ◽  
Clayton F. Giese ◽  
W. Ronald Gentry
Keyword(s):  
Wave Function ◽  
Binding Energy ◽  
Vibrational Wave Function
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