From: Stuart Armstrong (firstname.lastname@example.org)
Date: Thu Feb 12 2009 - 03:49:27 MST
>> the probability is NOT the square
>> of the (complex valued) wave function
> The complex valued wave function, also called the quantum wave function,
> is the square root of a probability.
Not, it isn't. http://en.wikipedia.org/wiki/Wave_function for
instance; note the modulus signs inside the integrals. The probability
is the squared MODULUS of the wave function, not the square of the
wave function itself.
>> Then you need to add a remark to get rid of the non-real phase changes
> If only I could. It would be nice indeed if you could get rid of the
> imaginary part of the quantum wave function, because then you'd also get
> rid of quantum weirdness, but as experiment has shown that's not the way
> the world works.
Sigh... A phase change is the multiplication of the wave function by a
unit complex number. In isolation, this phase change has no actual
consequences (multiplying your whole wave function by i changes
nothing) - only the relative phase difference of two waves can be
Here is measured the relative phase between the original system and
doing the interchange twice - since two interchanges is the same as
doing nothing, the relative phase difference has to be 1. Hence the
phase change of doing the substitution once has to square to 1, ie be
1 or -1. Then the rest of the argument can proceed.
You have a good intuitive grasp of quantum mechanics, but you need to
brush up on the mathematics.
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