Ok so I'm currently revising my quantum theory course from this year and I've reached the section on the postulates for measurements in quantum mechanics. The one I'm having trouble with is "The only result of a precise measurement of some observable A is one of the eigenvalues of the corresponding operator [itex]\hat{A}[/itex]."(adsbygoogle = window.adsbygoogle || []).push({});

My main conceptual problem with this is that suppose I'm measuring the energy of some particle, it has an infinite number of values of energy I could measure it at, which suggests that the associated operator has an infinite number of eigenvalues. Is this just a natural consequence of working in an infinitely-dimensional Hilbert space, in which case how is the fact that we have 3-spacial dimensions encoded; or am I misunderstanding the nature of continuous basis vectors?

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# Measurements in Quantum mechanics

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