Let where ? ? and ? ? ? are the annihilation and creation operators of two independent

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

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Modern Quantum Mechanics

ISBN: 978-0201539295

Revised Edition

Authors: J.J Sakurai

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Question Posted: Apr 16, 2011 06:41 AM

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Let where ? ? and ? ? ? are the annihilation and creation operators of two independent

Question:

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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We know that aa 1 and aa aa 0 since oscillators are inde pendent then JJ aaaa aaa...View the full answer

Modern Quantum Mechanics

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