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- W2055622010 abstract "The problem of precise estimation of the low-lying discrete energy spectrum of quantum dots was addressed rigorously by means of the methods of upper and lower bounds for eigenvalues of linear Hermitian operators in Hilbert space. It was shown that the method of intermediate problems for eigenvalues and the classical Rayleigh–Ritz method may be fused into effective tool of analytical and numerical investigation of the energy spectrum of quantum dots thus enabling and facilitating calculation of eigenvalues with controlled or prescribed precision. As an example, the energy spectrum problem for a simple two-electron quantum dot with harmonic-oscillator spherical confinement potential was thoroughly analyzed. Precise numerical calculations corroborated that in the absence of external magnetic field the ground state of the dot is the spin singlet for quantum dots of arbitrary characteristic size, so that no spontaneous singlet-triplet phase transition can occur." @default.
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- W2055622010 date "2004-01-20" @default.
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- W2055622010 title "ON LOWER AND UPPER BOUNDS FOR ENERGY EIGENVALUES OF QUANTUM DOTS" @default.
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- W2055622010 doi "https://doi.org/10.1142/s0217979204023805" @default.
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