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The Pauli spin matrices are given by 01 = c) 02 = d) P 03 = a) Without actually finding the eigenvalues, explain why we should expect the eigenvalues of each of these matrices to be real. 69 b) Using just the determinant and trace of these matrices show that they must all have eigen- values +1 and -1. Show that these matrices do not commute: specifically, show that 0102 - 0201 = 2103, 02030302= 2i01, 0301-0103 = 2102. What does the previous result imply on whether or not these matrices share common eigen- vectors?

The Pauli spin matrices are given by 01 = c) 02 = d) P 03 = a) Without actually finding the eigenvalues, explain why we should expect the eigenvalues of each of these matrices to be real. 69 b) Using just the determinant and trace of these matrices show that they must all have eigen- values +1 and -1. Show that these matrices do not commute: specifically, show that 0102 - 0201 = 2103, 02030302= 2i01, 0301-0103 = 2102. What does the previous result imply on whether or not these matrices share common eigen- vectors?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The Pauli spin matrices are given by -61₁²-1₁-6-9 02 = 01 = c) 03 = a) Without actually finding the eigenvalues, explain why we should expect the eigenvalues of each of these matrices to be real. b) Using just the determinant and trace of these matrices show that they must all have eigen- values +1 and -1. 2003, Show that these matrices do not commute: specifically, show that 0102 - 0201 = 02030302 = 2i01, 0301-0103 = 2i02. d) What does the previous result imply on whether or not these matrices share common eigen- vectors?
Transcribed Image Text:The Pauli spin matrices are given by -61₁²-1₁-6-9 02 = 01 = c) 03 = a) Without actually finding the eigenvalues, explain why we should expect the eigenvalues of each of these matrices to be real. b) Using just the determinant and trace of these matrices show that they must all have eigen- values +1 and -1. 2003, Show that these matrices do not commute: specifically, show that 0102 - 0201 = 02030302 = 2i01, 0301-0103 = 2i02. d) What does the previous result imply on whether or not these matrices share common eigen- vectors?
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