Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.issp.ac.ru/lnep/bulaev/spintronics/Spintronics-A1.pdf Дата изменения: Fri Mar 21 18:09:26 2008 Дата индексирования: Tue Oct 2 12:26:00 2012 Кодировка: Поисковые слова: south pole

Spintronics in Nanostructures Assignment 1

SS 2007 Handing in on Monday 02.04.07

Assistant: Mircea Trif ­ Office 4.4 ­ Tel. 061 267 36 56 ­ Mircea.Trif@unibas.ch

Exercise 1. Proof the following theorems: a) A group has only one identity element. b) Every element of a group has only one inverse.

Exercise 2. a) b) c) d) What are the symmetry operations of a regular hexagon? What is the order of the point group of it? What is the order of all elements of the group? Find the classes. Why are not all the two-fold axes in the same class?

Exercise 3*. Consider the point group Td (full symmetry of the tetrahedron). a) Find all elements of the group and determine the order of the group. b) Determine the order of the elements of Td . c) Find the classes of Td .

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