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While the dynamics for three-dimensional axially symmetric two-electronquantum dots with parabolic confinement potentials is in general non-separablewe have found an exact separability with three quantum numbers for specificvalues of the magnetic field. Furthermore, it is shown that the magneticproperties such as the magnetic moment and the susceptibility are sensitive tothe presence and strength of a vertical confinement. Using a semiclassicalapproach the calculation of the eigenvalues reduces to simple quadraturesproviding a transparent and almost analytical quantization of the quantum dotenergy levels which differ from the exact energies only by a few percent.Comment: 10 pages, 1 figure (gif), 3 figures (eps

Semiclassical analysis of a two-electron quantum dot in a magnetic field: Dimensional phenomena