Consider the wave packet defined by c1x2 = L q 0 B1k2cos
Chapter 40, Problem 40.42(choose chapter or problem)
Consider the wave packet defined by c1x2 = L q 0 B1k2cos kxdk Let B1k2 = e-a2 k2 . (a) The function B1k2 has its maximum value at k = 0. Let kh be the value of k at which B1k2 has fallen to half its maximum value, and define the width of B1k2 as wk = kh. In terms of a, what is wk? (b) Use integral tables to evaluate the integral that gives c1x2. For what value of x is c1x2 maximum? (c) Define the width of c1x2 as wx = xh, where xh is the positive value of x at which c1x2 has fallen to half its maximum value. Calculate wx in terms of a. (d) The momentum p is equal to hk>2p, so the width of B in momentum is wp = hwk>2p. Calculate the product wpwx and compare to the Heisenberg uncertainty principle.
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