I was reading about Casimir effect from David Tong's QFT notes and I was struggling to understand one thing.
At page 27, equation (2.33) describes the energy in between the plates, then why does the writer says that the energy outside the plates is $E(L-d)$?
Well, since the $x$-axis (which is normal to the plates) is periodic, the words inside and outside the 2 plates should be taken with a grain of salt. The main point is that the 2 plates separate the bulk into 2 regions of thickness $d$ and $L\!-\!d$, resprectively, and we should take the vacuum energy $E(d)$ and $E(L\!-\!d)$ of both regions into account.
