We make use of an e®ective Hamiltonian which succeeds in mapping surface configurations
to potential formulations to study the two dimensional quantum wells with rough
interfaces. We investigate two types of surface configurations: point defects and real random
roughness. We also study two roughness e®ects including local changes of widths as
well as curvature e®ect. In eigenlevel statistics we find the distributions of nearest level
spacings satisfy well the interpolation formula given by Izrailev, and thus we obtain the
ensemble average specific heat in low temperature limit is proportional to T1+°, where °
is the fitting parameter of the Izrailev formula and is related to the Fermi level. And in
eigenfunction statistics, the localization property is described better by the scaling behavior
of participation numbers than by the participation numbers only. The connection
between eigenlevel statistics and eigenfunction statistics is also verified.

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