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Suppose that the two operators A and B satisfy the commutation relation [A, B] = B....

Suppose that the two operators A and B satisfy the commutation relation [A, B] = B. Let |a > is an eigenvector
of A with an eigenvalue a, i.e. A|a >= a|a >. Show that vector B|a > is also an eigenvector of A, and find the
corresponding eigenvalue.

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