I'm having to essentially piece together a framework of background knowledge to understand parts of a QM class in which I'm lacking prerequisites; one of the things that I noticed that really confused me was the square of the momentum operator <p>, and how that translated into the integrand of an expectation value; Squaring an operator as far as I'm as aware isn't as simple as just squaring its components, because, for the momentum operator defined as [tex] \langle p^2 \rangle = \int_{-\infty}^{\infty}\psi^*(x)p^2\psi(x) = \int_{-\infty}^{\infty}\psi^*(x)\bigg(-\hbar^2 \frac{\partial^2}{\partial x^2}\psi(x)\bigg)[/tex](adsbygoogle = window.adsbygoogle || []).push({});

The differential part of the operator changed, too! This isn't just squaring, what is it? [tex] \frac{d}{dx}\frac{d}{dx} \neq \frac{d^2}{dx^2} [/tex] If I'm given some arbitrary operator A and told to calculate [tex] \langle A^2\rangle [/tex] How do I know what the operator "squared" takes the form of?

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# I How exactly does squaring operators (e.g. <p^2> work?

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