The doubt: It's not a problem, but a doubt. We know that in general quantum physics at undergraduate level, we write pΨ = (ħ/i) dΨ/dx. My doubt is that if we derived this equation from Schrodinger's equation only, so we must operate p on a wave-function only, which satisfies Schrodinger's equation. But I went further, and I saw a problem in the book - "Concepts of Modern Physics - A. Beiser", Chapter 5, Problem 9. It was asked to find the value of <xp>-<px>. Now to solve the problem, p is operated on xΨ (for <px>) and Ψ (for <xp>) both simultaneously. But I can prove that if Ψ satisfies Schrodinger's equation, xΨ cannot. So how can we operate p on xΨ, when it doesn't satisfy the Schrodinger's equation. Or may be p can operate on anything, then we need a proof, which I may have not yet studied, is it true that there exists such a proof? Please someone help.