4. Prove that if there are two operators A, ˆ Bˆ, such thattheir commutator [A, ˆ Bˆ] = λ whereλ is a constant. Show that (6 points)
exp[μ(Aˆ + Bˆ)] = exp(μAˆ) exp(μBˆ) exp(−μ2λ/2)
where given an operator Xˆ; exp(tXˆ) = 1 + tXˆ +12t2Xˆ 2 + ... +1n!tnXˆ n + ... (the usual
exponential series implemented for operators).
Join us to gain access to millions of questions and expert answers. Enjoy exclusive benefits tailored just for you!
(Save $1 )
One time Pay
(Save $5 )
Billed Monthly
*First month only
You can see the logs in the Dashboard.
