On the Energy Spectrum of Two-Electron Quantum Dot in External Magnetic Field

A method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, is applied to investigation of the energy spectrum and eigenstates of a two-electron two-dimensional quantum dot (QD) formed by a parabolic confining potential in the presence of external magnetic field. It is shown that this method, being supplemented with conventional Rayleigh-Ritz variational method and stochastic variational method, provides an efficient tool for precise calculation of the energy spectrum of various models of quantum dots and helps to verify results obtained so far by various analytical and numerical methods being of current usage in numerous theoretical studies of quantum dots.