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

• Veröffentlicht in: Condensed Matter Physics
• Datum: 2006
• Hauptverfasser: Soldatov, A.V., Bogolyubov, N.N., Kruchinin, S.P., Jr.
• Format: Artikel
• Sprache: English
• Veröffentlicht: Інститут фізики конденсованих систем НАН України 2006
• Online Zugang: https://nasplib.isofts.kiev.ua/handle/123456789/121309
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Zitieren: 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.