PH 253 Midterm: ph253_F10_Exam_2_SOLN
Document Summary
Ph 253 exam 2: solutions: given the wave function (a) find n needed to normalize . (b) find hxi, hx2i, and x. In order to normalize the wavefunction, we need to split up the usual integral into two integrals over. [ , 0] and [0, ] since the function is de ned separately over those intervals. Since the wave function is piecewise continuous, this need not trouble us though. Next, we nd hxi in the usual way, again taking care to split the integral into two bits: x| |2 dx = hxi = z xn2e2 x dx + z. By symmetry, the two integrals are equal in magnitude and opposite in sign, so the expected position is at the origin. Finding hx2i requires only a bit more math: x2n2e2 x dx + z x2n2e 2 x dx x2| |2 dx = (6) (2) (3) (4) (5) (7) (8) (9) hx2i = z.
