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Journal ArticleDOI

Calculation of Matrix Elements for One‐Dimensional Quantum‐Mechanical Problems

01 Nov 1968-Journal of Chemical Physics (American Institute of Physics)-Vol. 49, Iss: 9, pp 4209-4211
TL;DR: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory using matrix elements was studied in this paper, where transformation theory was used to solve the problem of matrix elements calculation.
Abstract: Matrix elements calculation for one dimensional quantum-mechanical problems using transformation theory
Citations
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Journal ArticleDOI
TL;DR: In this article, a review of the multiconfiguration time-dependent Hartree (MCTDH) method for propagating wavepackets is given, and the formal derivation, numerical implementation, and performance of the method are detailed.

2,053 citations

Journal ArticleDOI
TL;DR: The formal definition of the generalized discrete variable representation for quantum mechanics and its connection to the usual variational basis representation (VBR) is given and the DVR is shown to be accurate in itself, and an efficient representation for optimizing basis set parameters.
Abstract: The formal definition of the generalized discrete variable representation (DVR) for quantum mechanics and its connection to the usual variational basis representation (VBR) is given. Using the one dimensional Morse oscillator example, we compare the ‘‘Gaussian quadrature’’ DVR, more general DVR’s, and other ‘‘pointwise’’ representations such as the finite difference method and a Simpson’s rule quadrature. The DVR is shown to be accurate in itself, and an efficient representation for optimizing basis set parameters. Extensions to multidimensional problems are discussed.

1,477 citations

Journal Article
TL;DR: Theorie des effets de couplage vibronique multimodes is described in this paper, where couplages mettant en jeu des modes and des etats degeneres.
Abstract: Mise au point. Theorie des effets de couplage vibronique multimodes. Probleme a 2 etats. Couplage vibronique mettant en jeu des modes et des etats degeneres. Effets du couplage vibronique multimodes en spectroscopie. Comportement statistique des niveaux d'energie vibroniques. Intersections coniques et evolution temporelle de la fluorescence

1,424 citations

Journal ArticleDOI
TL;DR: In this paper, a new method for the calculation of bound state eigenvalues and eigenfunctions of the Schrodinger equation is presented, which is derived from the discrete Fourier transform algorithm.
Abstract: A new method for the calculation of bound state eigenvalues and eigenfunctions of the Schrodinger equation is presented. The Fourier grid Hamiltonian method is derived from the discrete Fourier transform algorithm. Its implementation and use is extremely simple, requiring the evaluation of the potential only at certain grid points and yielding directly the amplitude of the eigenfunctions at the same grid points.

951 citations

Journal ArticleDOI
TL;DR: In this article, the multiconfigurational timedependent Hartree (MCTDH) approximation to the timedependent Schrodinger equation is tested for a realistic three-dimensional example, the photodissociation of NOCl.
Abstract: The multiconfigurational time‐dependent Hartree (MCTDH) approximation to the time‐dependent Schrodinger equation is tested for a realistic three‐dimensional example, the photodissociation of NOCl. The working equations of the MCTDH scheme introduced earlier are discussed in some detail. A computational scheme is presented which allows for efficient numerical MCTDH calculations. This scheme is applied to the photodissociation of NOCl after excitation to the S1 surface. The results are compared to the results of an exact wave‐packet dynamics calculation. Fast convergence of the MCTDH results toward the exact one is found as the number of configurations is increased. The computation times of the MCTDH calculations are found to be much shorter than those of the exact calculation. Even MCTDH calculations including sufficiently many configurations for a fully converged (quasiexact) description require over two orders of magnitude less CPU time than an exact calculation. The so‐called ‘‘natural populations’’ tha...

872 citations

References
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