In this problem you will establish the correspondence between Equations 6.30 and 6.31. (a) Diagonalize the matrix
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In this problem you will establish the correspondence between Equations 6.30 and 6.31.
(a) Diagonalize the matrix
to obtain the matrix M' = SMS-1 where S-1 is the unitary matrix whose columns are the (normalized) eigenvectors of M.
(b) Use the binomial expansion to show that limN→∞ (M')N is a diagonal matrix with entries e-iφ and eiφ on the diagonal.
(c) Transform back to the original basis to show that
agrees with the matrix in Equation 6.31.
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Related Book For
Introduction To Quantum Mechanics
ISBN: 9781107189638
3rd Edition
Authors: David J. Griffiths, Darrell F. Schroeter
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