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The term is related to the famous Wave-particle Duality , according to which a Particle (a "small" physical object) may display either particle or wave aspects, depending on the observational situation. Or, indeed, a variety of intermediate aspects, as the situation demands.

This "transformation" idea also refers to the changes a physical object may undergo in the course of time, whereby it may "move" between "positions" in its Hilbert "space".

Remaining in full use today, it would be regarded as a topic in the mathematics of Hilbert Space , although technically speaking it is somewhat more general in scope. While the terminology is reminiscent of motion in ordinary space, the Hilbert space of a quantum object is more general, and holds its entire Quantum State .