Consider the wave packet defined by

Let B(k) = e €“ a2k2 (a) The function B(k) has its maximum value at k = 0. Let kh, be the value of k at which B(k) bas fallen to half its maximum value, and define the width of B(k) as wk = kh. In terms of α, what is wk?
(b) Use integral tables to evaluate the integral that gives ψ (x). For what value of x is ψ (x) maximum?
(c) Define the width of ψ (x) as wx = xh, where xh is the positive value oh where ψ(x) bas fallen to half its maximum value. Calculate w. in terms of α.
(d) The momentum p is equal to hk/2π, so the width of B in momentum is wp = hwk/2π. Calculate the product wp wx and compare to the Heisenberg uncertainty principle.

Transcribed Image Text:

#(x) = | B(k) coskr dk