- #1
taishizhiqiu
- 63
- 4
Although strictly quantum mechanics is defined in ##L_2## (square integrable function space), non normalizable states exists in literature.
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?
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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