Browsing by Author "Taddese, Hiruy"

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    Time Dependent Quantum Mechanical Approach : Case Studies of Ammonia Molecule
    (Addis Ababa University, 2009-06) Taddese, Hiruy; Mengistu, Gizaw (PhD)
    The aim of this thesis work is to implement time dependent Quantum mechanical approaches to study inversion phenomena of ammonia Molecule. This approaches will enable us visualize the time evolution of the orientation of the molecule inside the symmetric double well potentials. To study this approach diffusion Quantum Monte Carlo(DQMC) method, which propagates the time dependent Schr¨odinger equation in imaginary time, had been used. Since solving the schr¨odinger equation exactly with double well potential is not possible, numerical approach had been used. In order to get each energy eigenstates, the time independent Schr¨odinger equation with symmetric double well potential had been descritised and changed in to eigenvalue problem. The QL and QR algorithm had been used to solve the eigenvalue problem giving us energy eigenstates. The wave functions corresponding to the eigen energy states had also been obtained. In addition to this, the quantum mechanical energy splitting effect had been studied for different symmetrical double well potentials. The diffusion function will be obtained as a linear combination of the product of wave function of the time independent eigenfunctions which decay exponentially in real time. The probability density, which shows where the Nitrogen atom is most probably to be found, being the square of the diffusion function. The full cycle of the ammonia‘s orientation inside the symmetric double well had been done for different time steps. Finally comparison between theoretical and computational results had been done for viii different time steps. The simulations shows that similar results had been found in both theoretical and computational approaches