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(1) The wavefunction is characterised as encoding all the physical characteristics of a particle. But which ones? The quantum numbers? In that case, since each quantum number ranges over discrete values, there would seem to be only a countably (as opposed to a continuum) of possible wave functions. Is this correct? If so, since the wave function gives probability amplitudes, can one therefore say that there are an uncountable number of probabilities excluded?

(2) Black hole entropy is considered to encode the information about the black hole. (Already wrong?) But entropy is a dimensionless number, and the amount of entropy is proportional to the area of a given black hole. So I do not see how entropy could act as an encoding for different combinations of these physical properties. If it does, what form does the encoding take? What quantities is it considered to encode: mass/energy of the black hole, its total spin, its angular momentum, its charge... anything else? Similarly to the first question, are there thus only a countable number of possible values that entropy for a black hole can take on, since none of those quantities are continuous?

Thanks for any pointers.

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# Number of possible wavefunctions only countably infinite?

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