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Why are quantities called operators

  1. Feb 5, 2012 #1

    dpa

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    Is it because measurement of those quantities involves action on the system.
    And is the idea that as light is to be used to measure momentum which effects its position fundamental of QM or is it merely like an analog to understand.
     
  2. jcsd
  3. Feb 5, 2012 #2

    tiny-tim

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    hi dpa! :smile:
    the quantity is not called an operator …

    its representation in quantum theory (in the equations) is called an operator, because it operates on the wave-function

    eg, momentum is represented by a derivative, which is obviousy an operator! :wink:
    no, the fundamental point is that when we measure both position and speed (in the same direction), there is a limit to the accuracy …

    the disturbance caused by light (or anything else) is merely a consequence of that :smile:
     
  4. Feb 5, 2012 #3

    dpa

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    tim,
    1. What causes the limit to accuracy.
    2. How does momentum operate. I mean momentum is an quantity, clasically internal to body and it's motion.
     
  5. Feb 5, 2012 #4

    tiny-tim

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    heisenberg's uncertainty principle
    momentum is a physical quantity, it doesn't operate
     
  6. Feb 5, 2012 #5

    dpa

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    sorry, i realize that I had not got something fundamental.
    Again,
    1. I meant to say how/why uncertainity principle. I mean, why is there uncertainity.
    2. So what's an operater.
     
  7. Feb 5, 2012 #6
    An operator is a mathematical object that operates in a given function.

    Operators are not quantities, but many quantities [itex]a[/itex] have associated an operator [itex]\hat{a}[/itex] and verify the eigenvalue equation ([itex]\Psi[/itex] is a function)
    [tex]\hat{a} \Psi = a \Psi[/tex]
    Light is not «used to measure momentum».
     
  8. Feb 5, 2012 #7

    tiny-tim

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    because that's how the universe is
     
  9. Feb 5, 2012 #8

    dpa

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    is that like saying einstein's GR is intuitive/imaginative.
     
  10. Feb 5, 2012 #9

    dpa

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    is that like saying einstein's GR is intuitive/imaginative.

    And i just read somewhere about this.
    What are operators/parameters/ observables.
     
  11. Feb 5, 2012 #10

    tom.stoer

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    There are a few basic axioms (or principles) in QM, some of them purely mathematical. One of them is that the arena for QM is a Hilbert space of states (with operators acting on these states). Another one is that observables are represented by self-adjoint operators. The Heisenberg uncertainty principle is nothing else but a purely geometric theorem that can be derived for any pair of self-adjoint operators. So it follows solely from the mathematical construction.

    A physical interpretation for the uncertainty in position x and momentum p can be given as follows: x- and p-representation of wave functions are related via a Fourier transformation; the uncertainty of x (p) is represented by the width of a wave functon in x- (p-) representation; the product of 'width in x times width in p' has a lower bound > 0; a sharper peak in x results in a growing width in p and vice versa.
     
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