On 7/29/2025 7:18 AM, Alan Grayson wrote:
Assuming we know all possible results of the measurements of a quantum
system, that is, the set of possible eigenvalues, and suppose we also
know the associated eigenfunctions, and we write the wf of the system
as a linear sum of eigenfunctions each multiplied by a complex
constant, is it mathematically assumed, or proven somewhere (perhaps
by Von Neumann), that these eigenfunctions are orthogonal and form a
basis for the Hilbert space in which they reside? TY, AG --
Yes, that's pretty much it. The physical system, including the ideal
measurement, is modeled by a certain Hilbert space in which the basis
states are the eigenfunctions the measurement. This is implicit in the
concept of an ideal measurement as one, which if immediately repeated on
the same system, returns the same value again.
Brent
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