Solvation effects on wavenumbers and absorption intensities of the OH-stretch vibration in phenolic compounds – electrical- and mechanical anharmonicity via a combined DFT/Numerov approach

2020 ◽  
Vol 22 (23) ◽  
pp. 13017-13029
Author(s):  
Manuel J. Schuler ◽  
Thomas S. Hofer ◽  
Yusuke Morisawa ◽  
Yoshisuke Futami ◽  
Christian W. Huck ◽  
...  
Keyword(s):  
Phenolic Compounds ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Intensity Pattern ◽  
Solvation Effects ◽  
Stretch Vibration ◽  
First Time ◽  
Grid Based

A previously measured oscillatory intensity pattern in phenolic compounds between different solvents was successfully reproduced for the first time, employing modern grid-based methods to solve the time-independent vibrational Schrödinger equation.

Orbital stability of standing waves for nonlinear fractional Schrödinger equation with unbounded potential

2019 ◽  
Vol 12 (03) ◽  
pp. 1950043
Author(s):  
Xiaohua Liu
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Standing Waves ◽  
Orbital Stability ◽  
Fractional Schrödinger Equation ◽  
Unbounded Potential ◽  
Nonlinear Fractional Schrödinger Equation ◽  
The Stability ◽  
First Time ◽  
Fractional Schrodinger Equation

In this paper, the orbital stability of standing waves for nonlinear fractional Schrödinger equation is considered. By constructing the constrained functional extreme-value problem, the existence of standing waves is studied. With the help of the orbital stability theories presented by Grillakis, Shatah and Strauss, the orbital stability of standing waves is determined by the sign of a discriminant. To our knowledge, it is the first time that the abstract orbital stability theories presented by Grillakis, Shatah and Strauss are applied to study the stability of solutions for fractional evolution equation.

A NEW METHODOLOGY FOR THE CONSTRUCTION OF OPTIMIZED RUNGE–KUTTA–NYSTRÖM METHODS

2011 ◽  
Vol 22 (06) ◽  
pp. 623-634 ◽  
Author(s):  
D. F. PAPADOPOULOS ◽  
T. E. SIMOS
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
First Integrals ◽  
New Method ◽  
Phase Lag ◽  
Nyström Methods ◽  
Algebraic Order ◽  
Runge Kutta ◽  
First Time ◽  
Zero Phase

In this paper, a new Runge–Kutta–Nyström method of fourth algebraic order is developed. The new method has zero phase-lag, zero amplification error and zero first integrals of the previous properties. Numerical results indicate that the new method is very efficient for solving numerically the Schrödinger equation. We note that for the first time in the literature we use the requirement of vanishing the first integrals of phase-lag and amplification error in the construction of efficient methods for the numerical solution of the Schrödinger equation.

scholarly journals An Alternative Approach to Solutions of the MGECSC Potential in Presence of External Electric Field

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
M. K. Bahar
Keyword(s):  
Schrödinger Equation ◽  
Electric Field ◽  
External Electric Field ◽  
Schrodinger Equation ◽  
Mathematical Structure ◽  
Wave Functions ◽  
Electric Field Effect ◽  
Electric Field Effects ◽  
Alternative Approach ◽  
First Time

For the first time the Schrödinger equation with more general exponential cosine screened Coulomb potential in the presence of external electric field is solved approximately and analytically by applying an ansatz to eigenfunction of corresponding Hamiltonian and then energy values and wave functions are obtained. Since this potential turns into four different potential cases when considering different cases of the parameters in the potential, energies and eigenfunctions for these four different potentials are already to be found by solving Schrödinger equation with MGECSC potential. Energy values and wave functions obtained by using different values of potential parameters for each of these four different potential are compared with the results of other studies. Since the obtained general solutions in this study have been found in the presence of external electric field, the external electric field effects on systems with the mentioned four different potentials are also easily investigated. One of advantages of the present results and method is that if external electric field is equal to zero, general mathematical structure of corresponding equations does not change and then electric field effect can be eliminated. The presence or absence of electric field does not prevent solving the Schrödinger equation analytically.

scholarly journals A New Algorithm for the Approximation of the Schrödinger Equation

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 628-642 ◽  
Author(s):  
Rong-an LIN ◽  
Theodore E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Computational Cost ◽  
Control Technique ◽  
Phase Lag ◽  
Step Method ◽  
Periodicity Analysis ◽  
Algebraic Order ◽  
The Stability ◽  
First Time

AbstractIn this paper a four stages twelfth algebraic order symmetric two-step method with vanished phase-lag and its first, second, third, fourth and fifth derivatives is developed for the first time in the literature. For the new proposed method: (1) we will study the phase-lag analysis, (2) we will present the development of the new method, (3) the local truncation error (LTE) analysis will be studied. The analysis is based on a test problem which is the radial time independent Schrödinger equation, (4) the stability and the interval of periodicity analysis will be presented, (5) stepsize control technique will also be presented, (6) the examination of the accuracy and computational cost of the proposed algorithm which is based on the approximation of the Schrödinger equation.

Some novel optical solutions to the perturbed nonlinear Schrödinger model arising in nano-fibers mechanical systems

2021 ◽  
Author(s):  
Onur Alp Ilhan ◽  
Jalil Manafian ◽  
Mehrdad Lakestani ◽  
Gurpreet Singh
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Three Dimensional ◽  
Dynamic Structure ◽  
Expansion Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Wave Solutions ◽  
First Time

This paper aims to compute solitary wave solutions and soliton wave solutions based on the ansatz methods to the perturbed nonlinear Schrödinger equation (NLSE) arising in nano-fibers. The improved [Formula: see text]-expansion method and the rational extended sinh–Gordon equation expansion method are used for the first time to obtain the new optical solitons of this equation. The obtained results give an accuracy interpretation of the propagation of solitons. We held a comparison between our results and those are in the previous work. The outcome indicates that perturbed NLSE arising nano-fibers is used in optical problems. Finally, via symbolic computation, their dynamic structure and physical properties were vividly shown by three-dimensional, density, and [Formula: see text]-curves plots. These solutions have greatly enriched the exact solutions of (2+1)-dimensional perturbed nonlinear Schrödinger equation in the existing literatures.

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