A particle is represented (at time t = 0) by the wave function

(a) Determine the normalization constant A.
(b) What is the expectation value of x?
(c) What is the expectation value of p?
(d) Find the expectation value of x².
(e) Find the expectation value of p².
(f) Find the uncertainty in x (σ_x).
(g) Find the uncertainty in p (σ_p).
(h) Check that your results are consistent with the uncertainty principle.

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4 (x, 0) = A (a²-x²), 0, -a ≤ x ≤ +a, otherwise.