2. You have a harmonic oscillator with frequency \omega and mass m. Find the following: (a) Matrix Elements: i. \langle n|X^3 - P^2|n+1\rangle ii. \langle n|X^3 + [X, P]|n\rangle iii. \langle n|X^6|n+69\rangle iv. \langle n|[X^2, P^2]|n\rangle (b) Find \langle X(t)\rangle if $|\psi(0)\rangle = (\sqrt{3})^{-1}(|0\rangle + |2\rangle + |4\rangle)$
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