show that the occupation probability at E=EF + ?E is equal to the non occupational probability at E=E-?EDocument Preview:KUVEMPU UNIVERSITY OFFICE OF THE DIRECTOR DIRECTORATE OF DISTANCE EDUCATION Jnana Sahyadri, Shankaraghatta577 451, Karnataka Phone: 08282-256426; Fax: 08282-256370; Website: www.kuvempuuniversitydde.org E-mails: ssgc@kuvempuuniversity.org; info@kuvempuuniversitydde.org TOPICS FOR INTERNAL ASSESSMENT ASSIGNMENTS (2010-11) Programme: M.Sc. PHYSICS (Previous) Note: Students are advised to read the separate enclosed instructions before beginning the writing of assignments. Out of 15 Internal Assignment marks per paper, 5 marks will be awarded for regularity (attendance) to Counseling/Contact Programme/Practical classes pertaining to the paper. Therefore, the topics given below are only for 10 marks each paper. Paper I: MATHEMATICAL METHODS AND CLASSICAL MECHANICS 1. a) A projectile is fired uphill over ground with slope at an angle ? to the horizontal. Find the direction in which it should be aimed to achieve the maximum range. 03 marks b) A particle describes the curve r n ? an cos n? under a force p towards the pole. Find the law of force? 02 marks 2. a) Using the complex variable techniques, evaluate the real integral ? ? ? ? ? d ? 20 25 4cos sin 03 marks b) Show that if im? m Q ?e? is a single valued, then m is an integer. 02 marks Paper II: QUANTUM AND STATISTICAL MECHANICS 1. A quantum particle confined to one dimensional box of width a is in its first exited state. What is the probability of finding the particle over an interval of (a/2) marked symmetrically at the centre of the box. 04 marks 2. Give the two normalized but non-orthogonal eigen function ? e?r ? ? 1 and ? re?r ? ? 31 . Construct a new function ? which is orthogonal to the first function and is normalised. 03 marks 3. Show that the entropy at absolute zero in a canonical ensambles can be expressed as 0 s ? k log g . Where 0 g is statistical weight of the ground state. 03 marks 2 Paper III: SOLID STATE PHYSICS 1. Show that the occupation probability at is equal to the nonoccupation probability Attachments: 189891MScP.pdf
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