Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature.(adsbygoogle = window.adsbygoogle || []).push({});

In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}##

##

\langle\psi_p|\psi_{p'}\rangle=\delta(p-p')

##

However, it is not easy calculating matrix elements this way. For example, how to calculate

##

A(k)=i\langle u(k)|\partial_k|u(k)\rangle

##

##A(k)## is actually berry connection in solid state band theory and ##u(k)## is periodic part of bloch wave function.

Can anyone tell me how to define this matrix elements?

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# Matrix elements of non-normalizable states

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