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Unformatted text preview: Homework #3 — PHYS 402 — Spring 2011 Deadline: Wednesday, February 23, 2011, in class Professor Victor Yakovenko Office: 2115 Physics Web page: http://www2.physics.umd.edu/ ~ yakovenk/teaching/ Textbook: David J. Griffiths, Introduction to Quantum Mechanics 2nd edition, Pearson Prentice Hall, 2005, ISBN 0-13-111892-7 Do not forget to write your name and the homework number! Be sure to answer all additional questions asked in this assignment! Total score is 28 points. Ch. 4 Quantum Mechanics in Three Dimensions 1. 6 points. We discussed in class that an arbitrary spinor χ = ( a,b ), where a and b are some complex numbers satisfying the normalization condition | a | 2 + | b | 2 = 1, can be always written in the form χ = a b ! = e iγ cos( α/ 2) e iβ/ 2 sin( α/ 2) e- iβ/ 2 ! , (1) where α , β , and γ are some real parameters. Notice that the number of free parameters is the same as for the two complex numbers a and b subject to the normalization condition....
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