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 x 2 (e) Find the expectation value of p 2 (f) Find the uncertainty in x ( x ) (g) Find the uncertainty in p ( p ) (h) Check that your results are consistent with the uncertainty principle 4 (x, 0) A (a x), 0, a x a, otherwise

Question: A particle is represented (at time t = 0) by the wave function (a) Determine the normalization constant A. (b) What is the expectation value

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

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

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

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