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In quantum mechanics, I can write the hamiltonian as ##\hat{H} = \hat{p}^{2}/2m + \hat{V}##. I am confusing with the definition of the operator ##\hat{V}##, who represents the potential energy. If the potential energy depend only on the position, is it correct write ##\hat{V} = V(\hat{x})##? And, assuming that ##V## can be expanded in a power series of ##\hat{x}##, and using ##\hat{x} | x \rangle = x | x \rangle##, can I write ##\hat{V} | x \rangle = V(x) | x \rangle##? I would like know if this things I wrote are correct. Does anyone know a book or article that talk about this?