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8.1.7 Eigenfunctions of $ \hat{p}$

The operator $ \hat{p}$ is - i$ \hbar$$ {\frac{\partial}{\partial x}}$. Solving the equation

- i$\displaystyle \hbar$$\displaystyle {\frac{d}{dx}}$$\displaystyle \phi$(x) = p0$\displaystyle \phi$(x), (8.14)

we get

$\displaystyle {\frac{d}{dx}}$$\displaystyle \phi$(x) = ip0/$\displaystyle \hbar$$\displaystyle \phi$(x), (8.15)

with solution

$\displaystyle \phi$(x) = eip0x/$\scriptstyle \hbar$ (8.16)

a ``plane wave''. As we have seen before these states aren't normalised either!



© 1998 Niels Walet, UMIST
Email Niels.Walet@umist.ac.uk