Information-Entropy Studies in Some Double Well and Central Potentials

Sarangi, Ronit (2017) Information-Entropy Studies in Some Double Well and Central Potentials. Masters thesis, Indian Institute of Science Education and Research, Kolkata.

PDF (MS dissertation of Ronit Sarangi (12MS108)) thesis_12MS108.pdf - Submitted Version Restricted to Repository staff only Download (2MB)

Abstract

Studies concerning information measures in quantum systems have been on the rise quite recently. In this work we have presented two specific information measures, Shannon and Rényi entropies' in double well and central potentials. Our primary motivation was to discern whether global properties like information measures can identify dynamic phenomena like tunneling, delocalization and such. Although, the studies on central potentials are incomplete as of now, we have presented an easy to understand and implement eigensolver and tested it on Hydrogen atom. Finally, we have confirmed that information measures like Shannon and Rényi entropies can identify quantum phenomena mentioned above and can be used as the indicators for the same. Also, it was concluded that such measures provide a better limit on information that the traditional uncertainty principle. Lastly, the method we employed to solve the Hydrogen atom Hamiltonian was confirmed to be accurate and stable for Coulomb potential at least. In the future we hope to solve other potentials with this method.

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