The problem of an electron in a quantum well is treated using the new ("mirror'') boundary conditions implying that the particle has a specular reflection from the well's boundaries. Solutions of the Schrodinger equation are obtained for some particular well's geometries when the variable separation method is applicable. The resemblance between the "mirror'' and periodic boundary conditions is discussed. Comparison of the results with some experimental data shows that this approach can provide a reasonably accurate (without any adjustable parameters) description of nanosystems, including those with non-traditional geometry. (c) 2008 Elsevier B. V. All rights reserved.