Both (i d/dx) and (-i d/dx ) are Hermitian. For some reason (-i d/dx ) is chosen to be the momentum operator, and the consequences are that [x,p]=ih (and not -ih), and that [tex]e^{ipx} [/tex] is an eigenvalue of momentum p (and not -p).(adsbygoogle = window.adsbygoogle || []).push({});

Is there any fundamental reason why [x,p] can't be -ih, and [tex]e^{ipx} [/tex] can't have an eigenvalue -p, so that the momentum operator can be (i d/dx) ?

When dealing with Fourier series, [tex]f(x)=\int d^3p \mbox{ } f(p) e^{-ipx} [/tex] would be incorrect, right? It would have to be [tex]f(x)=\int d^3p \mbox{ } f(p) e^{ipx} [/tex] if you choose (-i d/dx )?

Do most math books use [tex]f(x)=\int d^3p \mbox{ } f(p) e^{-ipx} [/tex] or [tex]f(x)=\int d^3p \mbox{ } f(p) e^{ipx} [/tex] for their definition of a Fourier series? Which convention do you use for a Fourier series?

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# Momentum and fourier series

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