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On the numerical solution of the multidimensional vibrational time-independent Schroedinger equation

✍ Scribed by J.R. Alvarez-Collado; Robert J. Buenker

Publisher
John Wiley and Sons
Year
1992
Tongue
English
Weight
663 KB
Volume
13
Category
Article
ISSN
0192-8651

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✦ Synopsis

A preliminary study of the capability of the finite difference and finite element methods (FDM, FEM) to evaluate eigenvalues of one-, two-, and three-dimensional self-adjoint operators is reported with reference to applications dealing with the description of vibrational levels. Results of harmonic oscillator model potentials and ab initio PES for the water molecule are obtained by using the FDM. In spite of the large matrices used, low accuracy, nonvariational results are found. A different method, based on FEM and normal coordinates, is therefore proposed. Two nearly harmonic cases are studied and it is shown that variational results with higher accuracy can be obtained with a moderate cost. The vibrational levels of the water molecule are also calculated in order to compare the results with those of the FDM treatment.

📜 SIMILAR VOLUMES

Numerical Solution of the two-dimensiona
Numerical Solution of the two-dimensional time independent Schrödinger Equation by symplectic schemes
✍ Th. Monovasilis; Z. Kalogiratou; T. E. Simos 📂 Article 📅 2004 🏛 John Wiley and Sons ⚖ 146 KB 👁 1 views

## Abstract The solution of the two‐dimensional time‐independent Schrödinger equation is considered by partial discretization. The discretized problem is treated as an ordinary differential equation problem and solved numerically by asymptotically symplectic methods. The problem is then transformed