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Fabio Trani - One of the best experts on this subject based on the ideXlab platform.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations.
    Journal of Computational Chemistry, 2018
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations
    arXiv: Quantum Physics, 2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation rule. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method.

  • Real-space grid representation of momentum and kinetic energy operators
    2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation $\left[\widehat{x},\widehat{p}\right] =i\hbar\widehat{I}$. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in a electronic structure calculation is an intrinsic feature of the finite difference method.

Domenico Ninno - One of the best experts on this subject based on the ideXlab platform.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations.
    Journal of Computational Chemistry, 2018
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations
    arXiv: Quantum Physics, 2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation rule. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method.

  • Real-space grid representation of momentum and kinetic energy operators
    2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation $\left[\widehat{x},\widehat{p}\right] =i\hbar\widehat{I}$. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in a electronic structure calculation is an intrinsic feature of the finite difference method.

Giovanni Cantele - One of the best experts on this subject based on the ideXlab platform.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations.
    Journal of Computational Chemistry, 2018
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators on discrete coordinate eigenkets |xn〉 defined on a uniform grid. Starting from the discretization of integrals involving canonical commutations, simple closed-form expressions of the matrix elements are obtained. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the derivative approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method. © 2018 Wiley Periodicals, Inc.

  • Real-space grid representation of momentum and kinetic energy operators for electronic structure calculations
    arXiv: Quantum Physics, 2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation rule. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in electronic structure calculations is an intrinsic feature of the finite difference method.

  • Real-space grid representation of momentum and kinetic energy operators
    2017
    Co-Authors: Domenico Ninno, Giovanni Cantele, Fabio Trani
    Abstract:

    We show that the central finite difference Formula for the first and the second derivative of a function can be derived, in the context of quantum mechanics, as matrix elements of the momentum and kinetic energy operators using, as a basis set, the discrete coordinate eigenkets $\vert x_n\rangle$ defined on the uniform grid $x_n=na$. Simple closed form expressions of the matrix elements are obtained starting from integrals involving the canonical commutation $\left[\widehat{x},\widehat{p}\right] =i\hbar\widehat{I}$. A detailed analysis of the convergence toward the continuum limit with respect to both the grid spacing and the approximation order is presented. It is shown that the convergence from below of the eigenvalues in a electronic structure calculation is an intrinsic feature of the finite difference method.

Mohebbiakbar - One of the best experts on this subject based on the ideXlab platform.

Mehdi Dehghan - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of a meshless method for the time fractional diffusion-wave equation
    Numerical Algorithms, 2016
    Co-Authors: Mehdi Dehghan, Mostafa Abbaszadeh, Akbar Mohebbi
    Abstract:

    In this paper a numerical technique is proposed for solving the time fractional diffusion-wave equation. We obtain a time discrete scheme based on finite difference Formula. Then, we prove that the time discrete scheme is unconditionally stable and convergent using the energy method and the convergence order of the time discrete scheme is O(ź3źź)$\mathcal {O}(\tau ^{3-\alpha })$. Firstly, we change the main problem based on Dirichlet boundary condition to a new problem based on Robin boundary condition and then, we consider a semi-discrete scheme with Robin boundary condition and show when βź+ź$\beta \rightarrow +\infty $ solution of the main semi-discrete problem with Dirichlet boundary condition is convergent to the solution of the new semi-discrete problem with Robin boundary condition. We consider the new semi-discrete problem with Robin boundary condition and use the meshless Galerkin method to approximate the spatial derivatives. Finally, we obtain an error bound for the new problem. We prove that convergence order of the numerical scheme based on Galekin meshless is O(h)$\mathcal {O}(h)$. In the considered method the appeared integrals are approximated using Gauss Legendre quadrature Formula. The main aim of the current paper is to obtain an error estimate for the meshless Galerkin method based on the radial basis functions. Numerical examples confirm the efficiency and accuracy of the proposed scheme.

  • Implicit Solution of a Two-Dimensional Parabolic Inverse Problem with Temperature Overspecification
    Journal of Computational Analysis and Applications, 2001
    Co-Authors: Mehdi Dehghan
    Abstract:

    Three different implicit finite difference schemes for solving the two-dimensional parabolic inverse problem with temperature overspecification are considered. These schemes are developed for indentifying the control parameter which produces, at any given time, a desired temperature distribution at a given point in the spatial domain. The numerical methods discussed, are based on the second-order (5,1) Backward Time Centered Space (BTCS) implicit Formula, and the second-order (5,5) Crank-Nicolson implicit finite difference Formula and the fourth-order (9,9) implicit scheme. These finite difference schemes are unconditionally stable. The (9,9) implicit Formula takes a huge amount of CPU time, but its fourth-order accuracy is significant. The results of a numerical experiment are presented, and the accuracy and central processor (CPU) times needed for each of the methods are discussed and compared. The implicit finite difference schemes use more central processor times than the explicit finite difference techniques, but they are stable for every diffusion number.