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Unformatted text preview: outcomes of a measurement of is infinite! incompatible operators The reason is that and are socalled incompatible operators, where (8.32) The way to show this is to calculate (8.33) for arbitrary . A little algebra shows that (8.34) In operatorial notation, (8.35) where the operator , which multiplies by 1, i.e., changes into itself, is usually not written. The reason these are now called ``incompatible operators'' is that an eigenfunction of one operator is not one of the other: if , then (8.36) If was also an eigenstate of with eigenvalue we find the contradiction . Now what happens if we initially measure with finite acuracy ? This means that the wave function collapses to a Gaussian form, (8.37) It can be shown that (8.38) from which we read off that , and thus we conclude that at best (8.39) which is the celeberated Heisenberg uncertainty relation....
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This note was uploaded on 11/09/2011 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.
 Fall '10
 DavidJudd
 Physics, Energy

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