The soluation of the dependent schrödinger equation by using real wave functions and its application to c+h2 reaction.

ABSTRACTMaster ThesisTHE SOLUTION OF THE TIME DEPENDENT SCHRÖDINGER EQUATION BY USINGREAL WAVE FUNCTIONS AND ITS APPLICATION TO C(1D)+H2 REACTIONlker ARMAĞANFırat UniversityGraduate School of Science and TechnologyDepartment of Physics2006, Page: 51In this study, the solution of the time-dependent Schrödinger equation based on usingthe real wave packet technique has been described and applied to three dimensionalC ( 1D ) + H 2 (ν , j ) → CH (ν ı , j ı ) + H reactive scattering.The Schrödinger equation at zero total angular quantum number has been solved byusing the functional mapping of the Hamiltonian operator and propagating only the real part of thewave function. The operation of the Hamiltonian operator on the wave function has been performed byFourier Transformation and Discrete Variable Representation techniques. The Fourier Grid analysismethod has been used to analyze the final wave function and extract the transition probabilities fromit. The partial cross sections for J>0 have been estimated by Capture method. The integral crosssections have been calculated by summing the partial cross sections over all J states and the thermalrate constants were calculated by Boltzmann averaging of the integral cross sections over all energies.In section 1, some basic concepts related to reaction kinetics have been discussed. Insection 2, quantum time-independent and time-dependent equations of motion have been derivedwhile in section 3 the nuclear and electronic motions have been separated. In section 4, the most usedmethods for the solution of the time-dependent Schrödinger equation have been explained in details.In section 5, three dimensional quantum mechanical equations of motion forC ( 1D ) + H 2 (ν , j ) → CH (ν ı , j ı ) + H reactive scattering have been derived and from the solutionsof these equations, the expressions for the state-to-state, state-to-all reaction probabilities, integralcross sections and thermal rate constants have been obtained. In section 6, the results obtained forC ( 1D ) + H 2 (ν , j ) → CH (ν ı , j ı ) + H reaction have been discussed.Keywords: Reactive Scattering, C(1D)+H2 Reaction , Cross Sections.