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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 equationonly, so we must operate p on a wave-functiononly, 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, xΨcannot. 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.

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# Homework Help: ^, the operators in quantum mecħanics

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