Question: Let where ? ? and ? ? ? are the annihilation and creation operators of two independent simple harmonic oscillator satisfying the usual simple harmonic

Let where ? _? and ?^?_? are the annihilation and creation operators of two independent simple harmonic oscillator satisfying the usual simple harmonic oscillator commutation relations. Prove

J. = (at a, - at a ), J = ha' a

J. = (at a, - at a ), J = ha' a z. N = a, a, + a a. %3! %3! h2 J? = 2 [J', J.] = 0, :-)MG)-} [J., J,]= hJ +1

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