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A comment on Wave-particle duality is the uncertainty principle in disguise. Parent comment

Re:Wave-particle duality is the uncertainty principle in dis... by quarterwave on Saturday December 20, 2014 @01:21AM (#8776007)
@obastani : very good comment.

Aside: If |Psi> is a state with wavefunction <x|Psi>, then is there a linear operator A such that <x|A|Psi> = log(<x|Psi>)?

Note: Logarithm of a complex function.

[ Parent | on HN ]
Re:Wave-particle duality is the uncertainty principle in dis... by filmor on Saturday December 20, 2014 @03:33AM (#8776160)
Well, the logarithm is all but linear. If there was such an A you'd have

   <x|A(|Psi> + |Chi>) = log(<x|(|Psi> + |Chi>))
                       = log(<x|Psi> + <x|Chi>)
                       = log(<x|Psi>) log(<x|Chi>)
                      /= <x|A|Psi> + <x|A|Chi>
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Re:Wave-particle duality is the uncertainty principle in dis... by throwaway183839 on Saturday December 20, 2014 @08:15AM (#8776557)
I don't think that

  log(a + b) = log(a) log(b)
is a rule I'm familiar with!
[ Parent | on HN ]
Re:Wave-particle duality is the uncertainty principle in dis... by filmor on Saturday December 20, 2014 @08:36AM (#8776599)
You're right, I messed that one up. But as

  log(a + b) /= log(a) + log(b)
in general, the result is still correct.
[ Parent | on HN ]
Re:Wave-particle duality is the uncertainty principle in dis... by quarterwave on Saturday December 20, 2014 @11:47AM (#8777082)
Yes, agree that log() wouldn't result from a linear operator.

The idea behind my question: does the Shannon entropic integral correspond to the L2 length of some projected state? Leading to a prescription to prepare a state with minimum uncertainty product of canonically conjugate physical quantities.

Afaik, in classical statistical physics the log() shows up when the N! in a binomial probability distribution limits to large N via the Stirling approximation. It would be interesting to find a different route for log() to enter the picture from a quantum standpoint.

All admittedly vague and hand waving speculation.

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