**Unformatted text preview: **computed as: ( 29 ( 29 a a m i p a a m x ˆ ˆ 2 ˆ ; ˆ ˆ 2 ˆ-= + = ⊥ ⊥ . (10 pts) (c) If the particle is at the first excited state, use the integration table to find x and p . (10 pts) (d) Use the promoter and the demoter to find x and p when the particle is at the first excited state. Compare the result in (c). (10 pts) (e) If the particle is only at the first three states with equal probability at t = 0 , write down the normalized wave function in the analytical form. (10 pts) (f) Following (e), use the promoter and demoter to compute x ˆ , p ˆ , x and p at t = 0 . Notice that the analytical form becomes much more manageable with ⊥ a ˆ and a ˆ . (20 pts) (g) Following (e), find x ˆ (t) and p ˆ (t) . Check whether m p dt x d ˆ ˆ = is always valid. (10 pts) 1...

View
Full
Document