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Identifier uch.chemistry.msc//2002chatzopoulos
Title Επίλυση του Χρονοεξαρτημένου Προβλήματος με την Μέθοδο Πεπερασμένων Διαφορών
Creator Chatzopoulos, Apostolis
Abstract The use of computers for solving the time-dependent problem provides us a powerful tool for studying molecular systems. An algorithm, suitable for such studies, developed based on i) the high order finite differences methods for evaluating the action of the hamiltonian operator on the wavefunction ii) the expansion of the propagator in Chebychev polynomials. The algorithm got tested using four 1-D potential models. Firstly a Morse and symmetric bonded potential were used. Eigenvalues were computed with high accuracy. The error was minimized to 0.1 wavenumbers. Efforts were made, with rather successful results, to reduce computational time without significant cost to the accuracy. Also eigenfunctions were extracted in a very accurate way, in comparison with the theoretical curves. A symmetric potential barrier was used to test the algorithm ability to propagate a wavefunction, in respect to its quantum characteristics. The wave propagation got monitored step by step, including the reflection on the barrier and the transmission through it. The reflection and transmission coefficients were measured with high accuracy. Using the information obtained by the three previous potentials, a double-well potential, with a barrier in its center, was used. When the wavefunction got transmitted through the barrier, the energy spectrum peaks splitting was observed and measured accurately. After these successful tests the algorithm was used to develop methodology for studying the energy localization in a 1-D chain of coupled anharmonic oscillators. The necessary coupling strength, in order to get the energy delocalized, was measured. This methodology can be expanded in longer chains with more realistic potential wells, in order to be used to examine biomolecular chains.
Issue date 2002-11-01
Date available 2002-12-05
Collection   School/Department--School of Sciences and Engineering--Department of Chemistry--Post-graduate theses
  Type of Work--Post-graduate theses
Permanent Link https://elocus.lib.uoc.gr//dlib/9/b/a/metadata-dlib-2002chatzopoulos.tkl Bookmark and Share
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