Show that the average momentum of a particle is zero.

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Chapter 6.7, Problem 5E

To determine

Show that the average momentum of a particle is zero.

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A particle in a box of length L is placed in the state (x) = x(L-x), which is not normalized. (a) Evaluate the area under the curve described by (x)|² by integrating this function from x = 0 to x = L. (b) If one then modifies (x) by multiplying it by a constant A so that y(x) = Ax(L − x), determine the value of A that normalizes this modified function if L = 1? (c) For a box with length L = 1.5, the normalization constant is determined to be A = 1.9876. Use this value and the formula for y(x) to determine the probability that the particle will be located between x = 0 and x = 0.8.

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A particle in a box of length L is placed in the state (x) = x(L− x), which is not normalized. (a) Evaluate the area under the curve described by (x)|2 by integrating this function from x = 0 to x = L. (b) If one then modifies (x) by multiplying it by a constant A so that y(x) = Ax(L − x), determine the value of A that normalizes this modified function if L = 1? (c) For a box with length L = 1.5, the normalization constant is determined to be A = 1.9876. Use this value and the formula for y(x) to determine the probability that the particle will be located between x = 0 and x = 0.8.