First of all, I'm new here, so please bear with me if the answer to my question can be found elsewhere, but I have been working a problem and searching for an answer for two weeks now without a complete solution. In Eisberg and Resnick chapter 5, problem 15, an essential part of the problem is to show that the expectation of xp is the complex conjugate of the expectation of px. I have everything worked out except for one small thing: In order to demonstrate that <xp> = <px>* the following indefinite integral solution must evaluate to zero: x*|psy|^2 evaluated from minus infinity to infinity = 0, assuming that psy is square integrable (vanishes to zero at minus infinity and infinity) Every which way I work that problem I get that this evaluation yields a positive number except for the trivial solution psy(x) = 0. |psy(x)|^2 is nonnegative and then when multiplying by x it is negative at x<0 and positive at x> 0, and equal and opposite. Therefore, x |psy|^2 from minus infinity to infinity = 2 x |psy(x)|^2 evaluated from 0 to infinity. The answer to this can be zero only if psy is everywhere zero. Another way to get this is to take d/dx of x*|psy(x)|^2 which yields: |psy(x)|^2 +2 x psy(x) d/dx psy(x) Both of those terms are necessarily even functions and therefore is an even function. So it is not odd and therefore the evaluation of its integral from minus infinity to infinity is zero for psy(x) = 0 only. I've tried to leave the term in, but only when it is zero can it be shown that <xp> + <px> yields a real result--otherwise you are left with an imaginary part/term. Obviously I am missing something. The question is what? Thanks in advance for any help!