A non-normalized probability density for the position of an atom along the x-axis is given by, p(x) x {-(x + 1)(x-7) for -1Å ≤ x ≤ 7 Å otherwise 0 where x is in [Å] and p is in [Ź¹]. (a) Sketch the non-normalized probability density. Normalize the probability density. (b) (c) What is the probability that the atom is at a position x ≤ 1 Å? (d) What is the average position of the atom, (x)? The energy of the atom as function of position is given by E (x) = 2x², where x is in [Å] and E is in [eV]. (e) What is the average energy of the atom, (E)?

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