Spectral properties of a short-range impurity in a quantum dot

The spectral properties of the quantum mechanical system consisting of a quantum dot with a short-range attractive impurity inside the dot are investigated in the zero-range limit. The Green function of the system is obtained in an explicit form. In the case of a spherically symmetric quantum dot, the dependence of the spectrum on the impurity position and the strength of the impurity potential is analyzed in detail. It is proven that the confinement potential of the dot can be recovered from the spectroscopy data. The consequences of the hidden symmetry breaking by the impurity are considered. The effect of the positional disorder is studied.Comment: 30 pages, 6 figures, Late

Approximation by point potentials in a magnetic field

We discuss magnetic Schrodinger operators perturbed by measures from the generalized Kato class. Using an explicit Krein-like formula for their resolvent, we prove that these operators can be approximated in the strong resolvent sense by magnetic Schrodinger operators with point potentials. Since the spectral problem of the latter operators is solvable, one in fact gets an alternative way to calculate discrete spectra; we illustrate it by numerical calculations in the case when the potential is supported by a circle.Comment: 16 pages, 2 eps figures, submitted to J. Phys.