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Electronic states in coupled quantum dots are studied numerically and qualitatively in this article. A second-order finite volume scheme based on uniform meshes is first developed to solve the three-dimensional Schrodinger equation. The scheme is used to solve the eigenvalue problem with more than 12 million unknowns. Using these efficient numerical tools, we study quantum structure induced interactions, with emphases on the effects of dot size and space layer thickness. The numerical experiments have predicted the phenomena that envelope functions become delocalized over two QDs and the energy levels show anticrossing behavior.

X-band ferromagnetic resonance (FMR) was used to characterize in-plane magnetic anisotropies in rectangular and square arrays of circular nickel and Permalloy microdots. In the case of a rectangular lattice, as interdot distances in one direction decrease, the in-plane uniaxial anisotropy field increases, in good agreement with a simple theory of magnetostatically interacting uniformly magnetized dots. In the case of a square lattice a four-fold anisotropy of the in-plane FMR field Hr was found when the interdot distance a gets comparable to the dot diameter D. This anisotropy, not expected in the case of uniformly magnetized dots, was explained by a non-uniform magnetization m(r) in a dot in response to dipolar forces in the patternedmagnetic structure. It is well described by an iterative solution of a continuous variation procedure. In the case of perpendicular magnetization multiple sharp resonance peaks were observed below the main FMR peak in all the samples, and the relative positions of these peaks were independent of the interdot separations. Quantitative description of the observed multiresonance FMR spectra was given using the dipole-exchange spin wave dispersion equation for a perpendicularly magnetized film where in-plane wave vector is quantized due to the finite dot radius, and the inhomogenetiy of the intradot static demagnetization field in the nonellipsoidal dot is taken into account. It was demonstrated that ferromagnetic resonance force microscopy (FMRFM) can be used to determine both local and global properties of patterned submicron ferromagnetic samples. Local spectroscopy together with the possibility to vary the tip-sample spacing enables the separation of those two contributions to a FMRFM spectrum. The global FMR properties of circular submicron dots determined using magnetic resonance force microscopy are in a good agreement with results obtained using conventional FMR and with theoretical descriptions.