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I would like to study the spectral theory of the Dirac Laplacian on a non-compact quotient of the hyperbolic plane by a discrete group (I am particularly interested in the simple case where the ...

The Anderson Model is given by the random Hamiltonian (as an operator on $l^2(\mathbb{Z}^d)$) $$ H_\omega = - \triangle + V(\omega) $$ where $V(\omega) \mid x \rangle = \omega(x) \mid x \rangle$ ...

Look at the Hilbert space $l^2( \mathbb{Z}) $ and let $A$ be a translation invariant band operator. I.e. if $\{ e_n \}_{n \in \mathbb Z} $ is the standard basis for $l^2( \mathbb{Z}) $ then it holds ...

Can someone please explain the following in mathematical language? "First of all, angular excitations only push the energy up, never down, so it is enough to analyze spherically symmetric s-waves....