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Addis Ababa University Libraries Electronic Thesis and Dissertations: AAU-ETD! >
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http://hdl.handle.net/123456789/2025
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| Title: | TIME DEPENDENT QUANTUM MECHANICAL APPROACH : CASE STUDIES OF AMMONIA MOLECULE |
| Authors: | HIRUY, TADDESE MENGISTU |
| Advisors: | Gizaw Mengistu, (PhD) |
| Keywords: | TIME DEPENDENT QUANTUM |
| Copyright: | Jun-2009 |
| Date Added: | 30-Apr-2012 |
| Publisher: | AAU |
| Abstract: | 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 ̈dinger equation
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in imaginary time, had been used.
Since solving the schr ̈dinger equation exactly with double well potential is not pos-
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sible, numerical approach had been used. In order to get each energy eigenstates,
the time independent Schr ̈dinger equation with symmetric double well potential had
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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
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different time steps. The simulations shows that similar results had been found in
both theoretical and computational approaches. |
| URI: | http://hdl.handle.net/123456789/2025 |
| Appears in: | Thesis - Physics
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