Question

(4) The Pauli spin matrices are a set of 3 complex 2 x 2 matrices that are used in quantum mechanics to take into account the interaction of the spin of a particle with an external electromagnetic field. σ2 10), (a) Find the eigenvalues and corresponding eigenvectors for all three Pauli spin matrices. Show all of vour work (b) In Linear Algebra, two matrices A and B are said to commute if AB BA and their commutator defined as [A, B] = AB-BA equals zero. If the commutator is nonzero, the two matrices are said to not commute. The Pauli spin matrices have very well defined commutator relationships, in that the commutator of any two of the Pauli spin matrices can be expressed in term of the third. Cal culate the following commutators and express them in terms of the appropriate spin matrix (i) lơi,02] (ii) Ισ2Aq (iii) lơ3'에

Answer 1

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