Some more practice with tensor products: If A B is the tensor product of an observable...

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Some more practice with tensor products: If A B is the tensor product of an observable A = At acting in Hilbert space and B = B acting Hilbert space , and f(x) is any real-valued function, then f(AB) is an observable acting on H & H. TRUE or FALSE? (A & B) = f(A) f(B). If true, demonstrate that it is true. If false, provide an explicit counter-example. Some more practice with tensor products: If A B is the tensor product of an observable A = At acting in Hilbert space and B = B acting Hilbert space , and f(x) is any real-valued function, then f(AB) is an observable acting on H & H. TRUE or FALSE? (A & B) = f(A) f(B). If true, demonstrate that it is true. If false, provide an explicit counter-example.

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