Free particle energy eigenfunctions are $A\exp{[i(Et-\textbf{p}\cdot\textbf{r})/\hbar]}$ are non-normalizable. To normalize them one introduces a procedure called 'box normalization' where one imposes periodic boundary condition (PBC). But isn't imposing PBC quite an ad hoc procedure for a free particle?
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I'm not sure in what context OP is asking, but the standard heuristic logic goes as follows: A physics experiment is typically conducted within a compact laboratory space, and it is assumed that the outcome does not depend significantly on what is outside this arena if it is big enough, i.e. it should not depend on what boundary conditions (BCs) that we impose.
If it doesn't depend on the choice of BCs, then pick the BCs that make the calculation easiest to perform, e.g. periodic BCs, even if physically implausible.
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