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Titlebook: Numerical Grid Methods and Their Application to Schr?dinger’s Equation; Charles Cerjan Book 1993 Springer Science+Business Media Dordrecht

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發(fā)表于 2025-3-21 19:05:38 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Numerical Grid Methods and Their Application to Schr?dinger’s Equation
編輯Charles Cerjan
視頻videohttp://file.papertrans.cn/669/668998/668998.mp4
叢書名稱Nato Science Series C:
圖書封面Titlebook: Numerical Grid Methods and Their Application to Schr?dinger’s Equation;  Charles Cerjan Book 1993 Springer Science+Business Media Dordrecht
描述The use of numerical grid methods to solve the Schrodinger equation has rapidly evolved in the past decade.The early attempts to demonstrate the computational viability of grid methods have been largely superseded by applications to specific problems and deeper research into more sophisticated quadrature schemes. Underpinning this research, of course, is the belief that the generic nature of grid methods can enjoy a symbiotic development with advances in computer technology, harnessing this technology in an effective manner. The contributions to this proceedings demonstrate these points in full: several appli- cations displayed creative use and extension of existing grid methodology; other research concentrated on the development of new quadrature schemes or mixed numerical meth- ods. The research represented ranges from highly specific spectral simulations of van der Waals complexs to general schemes for reactive scattering. The novelty of grid methods in Density Functional Theory calculations should also be highlighted since it represents an alternative to standard basis set expansion techniques and might offer distinct advantages to the standard techniques. A deliberate attempt
出版日期Book 1993
關(guān)鍵詞Atom; molecule; scattering; spectra; structure
版次1
doihttps://doi.org/10.1007/978-94-015-8240-7
isbn_softcover978-90-481-4308-5
isbn_ebook978-94-015-8240-7Series ISSN 1389-2185
issn_series 1389-2185
copyrightSpringer Science+Business Media Dordrecht 1993
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Numerical Grid Methods and Their Application to Schr?dinger’s Equation978-94-015-8240-7Series ISSN 1389-2185
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An Adiabatic Pseudo-Spectral Representation of Multidimensional Molecular Potentials,The Adiabatic Pseudo-Spectral approach is reviewed in the context of collocation schemes for numerical grid operator representation. The power of this technique is demonstrated in its ability to construct spectral information for the HCN molecule in a specific energy range.
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The Multi-Configuration Hartree Approach,The multi-configuration time-dependent Hartree (MCTDH) approximation for solving the time-dependent Schr?dinger equation is derived. Its relation to other approaches as well as approximations to the MCTDH equations are discussed.
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Fast Pseudospectral Algorithm in Curvilinear Coordinates, formal properties connecting these two descriptions. Favorable numerical scaling of the matrix manipulations is demonstrated for the discrete representation. The advantages of partial summation are explored and applied to the specific case of non-direct product representations of the spherical Laplacian operator.
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Lobatto Shape Functions,on of the Kohn variational principle. The variational basis and discrete variable versions of the theory are both discussed, and shown to be equivalent respectively to high order finite element and finite difference schemes for integrating the Schr?dinger equation.
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