801 実空間での有限要素分割による時間依存シュレディンガ-方程式の解法

概要

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The conventional ab-initio calculation is performed by the spectral method based on the plane waves, and needs extremely high computational cost to realize sufficiently accurate analysis. Presented here is a new formulation of the quantum mechanical analysis based on the finite element method. The presented method can minimize the degrees of freedom for calculation, and does not need the Fourier transformation. The computational cost, therefore, seems to be drastically reduced. For the sake of mathematical simplicity, the problem of an electron of the ground state or the time evolution in the simple Coulomb potential are employed in the proposed formulation. The variational forms of the time-dependent and time-independent Schrodinger equations are individually derived by means of the weighted residual method. The finite element is formulated in line with the descritization of the variational forms by conventional shape functions.
一般社団法人日本機械学会の論文
2002-09-20