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Localisation of Low Energy Eigenfunctions to the Schr ?odinger Operator

Zhang, Wenqi

Description

We explore the phenomena where low energy eigenfunctions of the operator L = - d + V for V 2 L1 concentrate on a small subset of the original domain, and decay exponentially outside of this region. We consider the function u solving the equation Lu = 1 and show that 1 u acts as an e ective potential, in the sense that one can show Z jrfj2 + V f2 = Z u2jr(f=u)j2 + 1 u f2: With this equality, it can be shown that the regions where 1 u < for some (small) eigenvalue approximately corresponds to...[Show more]

CollectionsOpen Access Theses
Date published: 2018
Type: Thesis (Honours)
URI: http://hdl.handle.net/1885/173625
DOI: 10.25911/5d9efb570d00c

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