Method of intermediate problems in the theory of Gaussian quantum dots placed in a magnetic field
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 r...
Збережено в:
| Дата: | 2006 |
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| Автори: | , , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут фізики конденсованих систем НАН України
2006
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| Назва видання: | Condensed Matter Physics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/121309 |
| Теги: |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | 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. |
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