Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field

• Published in: Condensed Matter Physics
• Date: 2006
• Main Authors: Soldatov, A.V., Bogolyubov, N.N., Kruchinin, S.P., Jr.
• Format: Article
• Language: English
• Published: Інститут фізики конденсованих систем НАН України 2006
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/121309
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field / A.V. Soldatov, N.N. Bogolyubov, Jr., S.P. Kruchinin // Condensed Matter Physics. — 2006. — Т. 9, № 1(45). — С. 151–159. — Бібліогр.: 18 назв. — англ.

Applicability of the method of intermediate problems to the investigation of the energy eigenvalues and eigenstates
 of a quantum dot (QD) formed by a Gaussian confining potential in the presence of an external magnetic
 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 interface
 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 spectrum
 and eigenstates of the Gaussian quantum dots, confining small-to-medium number of excess electrons,
 with controllable or prescribed precision.