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PG Exam 2017 : Physics (Banaras Hindu University (BHU), Varanasi )

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Brijmohan
Banaras Hindu University (BHU), Varanasi
PhD Condensed matter Physics

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fiziks Institute for NET/JRF, GATE, IIT-JAM, JEST, TIFR and GRE in PHYSICAL SCIENCES MATEMATICAL PHYSICS SOLUTIONS NET/JRF (JUNE-2011) Q1. The value of the integral dz z 2 e z , where C is an open contour in the complex z -plane as C lm z shown in the figure below, is: (a) (b) e (c) Ans: 5 e e 5 e e (d) 5 e 0,1 C 5 e e 1,0 (c) 1,0 Re z Solution: If we complete the contour, then by Cauchy integral theorem 2 z 2 z 2 z 2 z 2 z z z dzz e dzz e 0 dzz e dzz e z e 2 ze 2e 1 1 1 Q2. 1 C C 1 1 Which of the following matrices is an element of the group SU 2 ? 1 1 (a) 0 1 1 i (b) 3 1 3 1 3 1 i 3 i 2 i (c) 3 1 i Ans: 5 e e (d) 3 2 1 2 1 2 3 2 (b) Solution: SU 2 is a group defined as following: SU 2 clearly (b) hold the property of SU 2 . 1 i 3 , 1 3 2 : , C; and 1 i 3 , 1 3 2 1 . Note: SU 2 has wide applications in electroweak interaction covered in standard model of particle physics. Head office fiziks, H.No. 23, G.F, Jia Sarai, Near IIT, Hauz Khas, New Delhi-16 Phone: 011-26865455/+91-9871145498 Website: www.physicsbyfiziks.com Email: fiziks.physics@gmail.com Branch office Anand Institute of Mathematics, 28-B/6, Jia Sarai, Near IIT Hauz Khas, New Delhi-16 1

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