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In this paper we consider the Anderson Hamiltonian with white noise potentialon the box $[0,L]^2$ with Dirichlet boundary conditions. We show that all theeigenvalues divided by $\log L$ converge as $L\rightarrow \infty$ almost surelyto the same deterministic constant, which is given by a variational formula.

Asymptotics of the eigenvalues of the Anderson Hamiltonian with white noise potential in two dimensions