1 V.A.Steklov Mathematical Institute,

Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigen-states of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external mag-netic field is discussed. Being smooth at the QD boundaries and of finite depth and range, this potential can only confine a finite number of excess electrons thus forming a realistic model of a QD with smooth inter-face between the QD and its embedding environment. It is argued that the method of intermediate problems, which provides convergent improvable lower bound estimates for eigenvalues of linear half-bound Hermitian operators in Hilbert space, can be fused with the classical Rayleigh-Ritz variational method and stochastic variational method thus resulting in an efficient tool for analytical and numerical studies of the energy spec-trum and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons, with controllable or prescribed precision. Key words: quantum dots, eigenvalues, eigenstates, upper and lower bound