A Laplace transform approach to find the exact solution of the $$N$$ N -dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

In this paper we obtain approximate bound state solutions of N -dimensional fractional time independent Schrödinger equation for generalised Mie-type potential, namely V (r α ) = A r 2α + B r α +C. Here α(0 < α < 1) acts like a fractional parameter for the space variable r. When α = 1 the potential converts into the original form of Mie-type of potential that is generally studied in molecular and chemical physics. The entire study is composed with Jumarie type fractional derivative approach. The solution is expressed via Mittag-Leffler function and fractionally defined confluent hypergeometric function. To ensure the validity of the present work, obtained results are verified with the previous works for different potential parameter configurations, specially for α = 1.At the end, few numerical calculations for energy eigenvalue and bound states eigenfunctions are furnished for a typical diatomic molecule.

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“…N acts the normalization constant as previous. These all outcomes in this subsection are well matched with the results [36].…”

Section: Mie-type Potential In N Dimension When α =supporting

confidence: 84%

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

Das¹,

Ghosh

Sarkar

et al. 2018

Journal of Mathematical Physics

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“…The effect of an electromagnetic field on a charged particle studied lot and in spite of its long history [23][24][25][26], still requires additional study in terms of different mathematical methods for various em field profiles. Motivated by these circumstances, in this paper we try to examine exact solutions of the KG equation for some different spatially-dependent em profiles by the means of the Laplace transformation method which is a very elegant technique, and can be used to transform a second order linear differential equation with coefficients that are linear in independent variable into a first order one [27][28][29][30]. Various useful properties of this integral transform ease out the scenario of finding energy eigenvalues and corresponding eigenfunctions.…”

Section: Introductionmentioning

confidence: 99%

Klein–Gordon equation for a charged particle in space-varying electromagnetic fields–A systematic study via the Laplace transform

Das¹,

Arda²

2017

Chinese Journal of Physics

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Exact solutions of the Klein-Gordon equation for a charged particle in the presence of three spatially varying electromagnetic fields, namely,2x 3 , are studied. All these fields are generated from a systematic study of a particular type of differential equation whose coefficients are linear in independent variable. The Laplace transform approach is used to find the solutions and the corresponding eigenfunctions are expressed in terms of the hypergeometric functions 1 F 1 (a ′ , b ′ ; x) for first two cases of the above configurations while the same are expressed in terms of the Bessel functions of first kind, J n (x), for the last case.

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“…Its solution play an essential part in the study of atomic and molecular structure and their spectral behavior. [1][2][3][4][5][6] There are various methods available in the literature for its solution such as Fourier transform method, [7][8][9] Nikiforov-Uvarov method, [10][11][12][13] asymptotic iteration method, [14][15][16][17][18][19][20][21] SUSYQM method, [22][23][24][25][26][27] Laplace transform method, [28][29][30][31][32][33][34] ansatz method, [3,6] and many more.…”

Section: Introductionmentioning

confidence: 99%

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

Rahman

2017

Int J of Quantum Chemistry

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We report an efficient and consistent method for the solution of Schrödinger wave equation using the Green's function technique and its successful application to the nonrelativistic radial wave equation of hydrogen atom. For the radial wave equation, the Green's function is worked out analytically by means of Laplace transform method and the wave function is proposed under the boundary conditions. Computationally the product of potential term, the proposed wave function and the Green's function are integrated iteratively to get the nonrelativistic radial wave function. The resultant wave after each iteration is normalized and plotted against the standard nonrelativistic radial wave function. The solution converges to the standard wave with the increasing number of iterations. Results are verified for the first 15 states of hydrogen atom. The method adopted here can be extended to many‐body problem and hope that it can enhance our knowledge about complex systems.

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A Laplace transform approach to find the exact solution of the $$N$$ N -dimensional Schrödinger equation with Mie-type potentials and construction of Ladder operators

Cited by 12 publications

References 33 publications

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

Time independent fractional Schrödinger equation for generalized Mie-type potential in higher dimension framed with Jumarie type fractional derivative

Klein–Gordon equation for a charged particle in space-varying electromagnetic fields–A systematic study via the Laplace transform

A Green's function approach to the nonrelativistic radial wave equation of hydrogen atom

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