Support for constants A and a (a) Determine A, by normalizing (x,0) (b) Find (x), (x 2 ), and x (at time t 0) (c) Find the momentum space wave function (p,0), and check that it is normalized (d) Use (p,0) to calculate (p), (p 2 ), and p (at time t 0) (e) Check the Heisenberg uncertainty principle for this state V(x,0) A z zx ( x )

Question: Support for constants A and a. (a) Determine A, by normalizing (x,0). (b) Find (x), (x 2 ), and x (at time t =

Support

V(x,0) = A .z"+zx (- < x < )

for constants A and a.
(a) Determine A, by normalizing Ψ(x,0).
(b) Find (x), (x²), and σ_x (at time t = 0).
(c) Find the momentum space wave function Φ(p,0), and check that it is normalized.
(d) Use Φ(p,0) to calculate (p), (p²), and σ_p (at time t = 0).
(e) Check the Heisenberg uncertainty principle for this state.

V(x,0) = A .z"+zx (- < x < )

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