The model of a wave and perfect classical walls works because it leads to getting an analytical solution the Schrodinger eqn. Another approach (Carolyne Van Vliet and William Duane) shows it's also just as valid to treat the walls as a superposition of states interacting with a localized particle…
… However, as Van Vliet pointed out (Quantization of linear momentum 1967), it's not amenable to a tidy solution. Ad-hoc moves such as collapse and many worlds result from adopting a model in which the particle behaves as a wave, partly based on the availability of a pathway to solve the equations.
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