Analytic matrix elements of the Schrödinger equation

Bhatti, Muhammad Iqbal

doi:10.12988/astp.2013.13002

Cited by 4 publications

(20 citation statements)

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Section: Introductionmentioning

confidence: 99%

“…The Fractional Bhatti polynomial (B-poly) technique [1,2] is extremely useful for solving varieties of differential equations. The fractional B-polys [2] are precise, define a basis set, straightforwardly differentiable and exemplify an arbitrary function to a desired accuracy over an interval. In recent years, many authors have predicted solutions of differential equations using analytic and numerical methods with high accuracy [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In recent years, many authors have predicted solutions of differential equations using analytic and numerical methods with high accuracy [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. In the past paper [2], an algorithm had been provided for solving fractional-order differential equations using a generalized Galerkin method and the B-poly basis of fractional-order. The method used the unitary property of generalized B-polys on the interval [0, R] and converted the differential equation into a matrix equation for constructing the solution of a fractional-order equation that provided agility to impose initial as well as boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

“…The method used the unitary property of generalized B-polys on the interval [0, R] and converted the differential equation into a matrix equation for constructing the solution of a fractional-order equation that provided agility to impose initial as well as boundary conditions. Several examples to determine the solutions of the fractional Harmonic Oscillator were provided [1][2][3][4][5]. In this paper, we will use a similar technique to solve fractional-order differential equation with variable coefficients.…”

Section: Introductionmentioning

confidence: 99%

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Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials

et al. 2018

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Solutions of a mathematical model for gas solubility in a liquid are attained employing an algorithm based on the generalized Galerkin B-poly basis technique. The algorithm determines a solution of a fractional differential equation in terms of continuous finite number of generalized fractional-order Bhatti polynomial (B-poly) in a closed interval. The procedure uses Galerkin method to calculate the unknown expansion coefficients for constructing a solution to the fractional-order differential equation. Caputo?s fractional derivative is employed to evaluate the derivatives of the fractional B-polys and each term in the differential equation is converted into a matrix problem which is then inverted to construct the solution. The accuracy and efficiency of the B-poly algorithm rely on the size of the basis set as well as the degree of the B-polys used. The fractional-order B-Poly technique has been applied to the mathematical model for a gas diffusion in a liquid with gas volume functions f (t)=1−t 1/2 and f (t)=1−t 3/2 . The solutions of the model were obtained which converged with a small number of B-polys basis set. In case of the power series solution, the solution did not converge due to alternating terms present in the solution. We used a Pade approximant on the power series solutions to extract the useful information which showed the solutions are convergent and those solutions were compared with the solutions obtained from the B-poly approach. Excellent agreement was found between the solutions. A Pade approximant was not used on the B-poly solutions because those were convergent with a smaller number of B-polys.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials

et al. 2018

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“…The B-spline basis functions of degree are piecewise polynomials defined on a knot sequence. When the number of B-splines is taken as , the basis set becomes a set of continuous B-polynomials over the range under consideration [32]. These B-polynomials are independent of the grid defined by knots and are simple algebraic polynomials.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Particle in Confined-Harmonic Potential in External Static Electric Field and Strong Laser Field

Lumb¹,

Prasad²

2013

JMP

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Dynamics of a particle in confined-harmonic potential, subjected to external static electric and time-dependent laser fields is studied. The energy levels and wave functions of unperturbed harmonic oscillator are evaluated using B-polynomial Galerkin method. Matrix formulation is used throughout the procedure. This procedure is very simple and efficient in comparison with other methods. Modifications of wave functions and energy levels due to static electric field are also calculated. Finally, absorption spectra of such a driven oscillator are studied and explained.

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Wide‐Gap Perovskite via Synergetic Surface Passivation and Its Application toward Efficient Stacked Tandem Photovoltaics

Huang

Wang

Nuryyeva

et al. 2021

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Superior bandgap tunability enables solution‐processed halide perovskite a promising candidate for multi‐junction photovoltaics (PVs). Particularly, optically coupling wide‐gap perovskite by stacking with commercially available PVs such as silicon and CIGS (also known as 4‐terminal tandem) simplifies the technology transfer process, and further advances the commercialization potential of perovskite technology. However, compared with matured PV materials and the phase‐pure FAPbI3, wide‐gap perovskite still suffers from huge voltage deficits. Here, the authors take advantage of the synergetic effect behind a sequential fluoride and organic ammonium salt surface passivation strategy to control non‐radiative energy losses, and obtained a 17.7% efficiency in infrared‐transparent wide‐gap perovskite solar cells (21.1% for opaque device), and achieved efficiencies of over 25% when stacked with commercial Si and CIGS products with original PCEs of 18–20% under a 4‐terminal working condition.

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Analytic matrix elements of the Schrödinger equation

Cited by 4 publications

References 0 publications

Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials

Solution of mathematical model for gas solubility using fractional-order Bhatti polynomials

Dynamics of Particle in Confined-Harmonic Potential in External Static Electric Field and Strong Laser Field

Wide‐Gap Perovskite via Synergetic Surface Passivation and Its Application toward Efficient Stacked Tandem Photovoltaics

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