Please help me with my homework. Ch7 #33 Evaluate the integral(7.65) <x> = 2/aa0xsin2(x / a) dx to give the average result<x> (the expectation value) foundwhen the position of a particle in the ground state of a right boxis measured many time. [hint: Rewrite sin2(x/a) in terms of cos(2x/a)and use integration by parts.] books answer is <x> = a/2 Ch7 #33 Evaluate the integral(7.65) <x> = 2/aa0xsin2(x / a) dx to give the average result<x> (the expectation value) foundwhen the position of a particle in the ground state of a right boxis measured many time. [hint: Rewrite sin2(x/a) in terms of cos(2x/a)and use integration by parts.] books answer is <x> = a/2
Explanation / Answer
use 2sin2 = 1 - cos(2) (2/a) x sin2(x/a) dx = (x/a) [1 - cos(2x/a)]dx = x/a dx - a/(2)2 [(2x/a)cos(2x/a)] d(2x/a) let 2x/a = (2/a) x sin2(x/a) dx = x/a dx -a/(2)2 cos d = x/a dx -a/(2)2 d(sin) = d[x2/(2a)] - a/(2)2[d(sin) - sin d] = d[x2/(2a)] - a/(2)2[d(sin) + d(cos)] integrate and get = x2/(2a) - a/(2)2(sin + cos) = x2/(2a) - a/(2)2 [2x/asin(2x/a) + cos(2x/a)] input limits and get = a/2