An algorithm for fractional Schrödinger equation in case of Morse potential

Abstract

Based on methods of numerical integration and Riemann–Liouville definition of the fractional derivatives, we find a numerical algorithm to find solutions of the time independent fractional Schrödinger equation for Morse potential or the quantum oscillator potential in one dimension, and the iteration formula is applied for multiple values of the fractional parameter of the space dependent fractional Schrödinger equation and multiple values of energy. We define and use the dimensionless form of the space dependent fractional Schrödinger equation of Morse potential. We employ the iteration formula of the time independent fractional Schrödinger equation of Morse potential to find the wave functions in the case of hydrogen chloride and hydrogen fluoride molecules for a certain value of the fractional parameter of the space dependent fractional Schrödinger equation and for many values of the dimensionless energy of each molecule.

The Generalized Fractional NU Method for the Diatomic Molecules in the Deng-Fan Model

“…[46], [48], [49]. As can be shown in Tables (10)(11)(12)(13)(14)(15), the ro-vibrational energy spectra of all selected DMs rise as the vibrational and rotational quantum numbers increase. Importantly, one can see that our estimates are perfectly consistent with prior works that used other techniques.…”

Эмпирические Критерии Качества Аппроксимации Электронного Терма Двухатомногой Молекулы Формулой Морза

“…По данным химической реферативной службы (Chemical Abstracts Service) на запрос " Формула Морза" выдаётся более 6000 ссылок. Как пример, приведём случайные выборки работ последнего времени в области спектроскопии [2][3][4][5][6][7][8][9][10][11][12][13], влияния внешнего поля, лазерной диссоциации молекул [14][15][16][17][18][19][20][21][22][23][24], термодинамики, кинетики [25][26][27][28][29][30][31][32][33][34], физики твёрдого тела и жидкости [35][36][37][38][39][40][41][42][43][44], межмолекулярных взаимодействий [45][46][47][48][49][50]…”

Numerical simulation of the space dependent fractional Schrödinger equation for London dispersion potential type

“…The linear fractional Schrödinger equation or the fractional Schrödinger equation is a type of the linear Schrödinger equations used in the fractional quantum mechanics and this equation use one of the physical potentials to give the probability. The fractional Schrödinger equation in the general space representation form with a space fractional parameter α is given in the linear formalism as follows [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 ]: Where h is Planck constant, Ψ( r ,t) is the wave function of the system in space-representation, j is the imaginary unit and is Hamiltonian operator in the fractional type which is defined by the following formula: K α is a coefficient, U ( r ) is the interaction potential of the system and is the space fractional operator which is given by: …”

“…The linear fractional Schr€ odinger equation or the fractional Schr€ odinger equation is a type of the linear Schr€ odinger equations used in the fractional quantum mechanics and this equation use one of the physical potentials to give the probability. The fractional Schr€ odinger equation in the general space representation form with a space fractional parameter α is given in the linear formalism as follows [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]:…”