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Title of Journal: Nuov Cim B

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Abbravation: Il Nuovo Cimento B (1971-1996)

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Società Italiana di Fisica

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1826-9877

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Magnetic bloch functions

Authors: F Bentosela
Publish Date: 2007/11/18
Volume: 16, Issue: 1, Pages: 115-126
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Abstract

Utilizing the lattice representation of OCR introduced by Zak for the treatment of the Schrödinger equation of an electron in the presence of an electrostatic periodic field and a uniform magnetic field this paper gives a decomposition of the space of states into spaces labelled by a constant of motionv1 Each of these spaces is constituted by functions that we shall call in analogy with the case without magnetic field the « magnetic Bloch functions » The constant of motionv1 is related to the set of coordinates of the centres of the classical orbits whick are coupled by the periodic potential and form the Pippard network The treatment is only valid for rational fluxess/N per lattice cellИспользуя решеточно е представление ССR введенное Заком для рассмотрения уравне ния Шредингера элект рона в электростатическом периодическом поле и однородном маг нитном поле в этой раб оте приводится разложен ие пространства состоя ний на пространства характеризуемые пос тоянной движения v1 Каждое из этих простр анств образовано фун кциями которые мы можем назв ать по аналогии со случае м отсутствия магнитн ого поля «магнитными блоховс кими функциями » Постоянн ая движения v1 соответ ствует системе координат це нтров классических орбит к оторые связаны посре дством периодического поте нциала и образуют структуру П иппарда Предложенно е рассмотрение справе дливо только для рациональных пот оков s/N на элементарную ячейкуFacendo uso della rappresentazione reticolare di CCR introdotta da Zak per il trattamento dell’equazione di Schrödinger per un elettrone in presenza di un oampo elettrostatico periodico e di un campo magnetico uniforme si dà in questo articolo la decomposizione dello spazio degli stati in spazi indicati da una costante del motov1 Ciaseuno di questi spazi è costituito da funzioni che in analogia al caso in oui non vi è campo magnetioo chiameremo « funzioni di Bloch magnetiche » La costante del motov1è in relazione all’insieme delle coordinate dei centri delle orbite classiche che sono accoppiate dal Potenziale periodico e formano la rete di Pippard Il trattamento è valido solo per flussi razionalis/N per cella del reticolo


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  2. N = 1,2 supergravities in 2 + 1 dimensions as Chern-Simons theories
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  8. Machian solution with matter injection in cosmology
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  12. Triplet correlations in model liquids
  13. Gravitational-wave tail in Einstein’s linear theory
  14. On the hypothesis that quantum mechanics has a nonlocal structure
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  18. Solution with third-order accuracy for the electron distribution function in weakly ionized gases and intrinsic semiconductors
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