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Do toy models of quantum mechanics help us better understand "regular" quantum mechanics? For example, if we look at quantum mechanics over a finite field $F$ (e.g. $\mathbb{Z}_2$), can this lead to new insights for "regular" quantum mechanics? Or do these toy models just help clarify our understanding of "regular" quantum mechanics without actually providing any new insight? In other words, what is the utility of having toy models of quantum mechanics?

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Toy Models of Quantum Mechanics

Do toy models of quantum mechanics help us better understand "regular" quantum mechanics? For example, if we look at quantum mechanics over a finite field $F$ (e.g. $\mathbb{Z}_2$), can this lead to new insights for "regular" quantum mechanics? Or do these toy models just help clarify our understanding of "regular" quantum mechanics without actually providing any new insight?