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Aug 24, 2017 at 14:20 comment added ZeroTheHero @SRA I've added a link to a paper that deals with some of the issues of your post.
Aug 24, 2017 at 14:00 history edited ZeroTheHero CC BY-SA 3.0
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Aug 24, 2017 at 13:44 comment added SRS I have added an addendum which really creates a confusion with this way of measuremnet.
Aug 24, 2017 at 13:43 history edited ZeroTheHero CC BY-SA 3.0
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Aug 24, 2017 at 13:41 history edited ZeroTheHero CC BY-SA 3.0
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Aug 24, 2017 at 13:07 comment added ZeroTheHero Basically yes since the operator $A$ acting on your state $\Psi$ results in a different wave function. Clearly average values for instance need not be the same for $\psi_A=A\Psi$ and $\psi_B=B\Psi$.
Aug 24, 2017 at 12:32 comment added SRS Do you mean the probability distribution changes and there is no meaning in comparing variances calculated from different probability distributions?@ZeroTheHero
Aug 24, 2017 at 12:29 history answered ZeroTheHero CC BY-SA 3.0