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Homework Help: Interpretation Schrödinger's formulae

  1. May 8, 2005 #1
    Dear Friends,

    Does anybodi knows the meaning, or anything related to the term:

    [tex] \Psi \nabla \Psi^* [/tex]

    or

    [tex] \Psi \nabla \Psi^* - \Psi^* \nabla \Psi [/tex]

    Is the representation of something in the reality?

    Best reggards.
     
  2. jcsd
  3. May 8, 2005 #2

    Galileo

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    If you have a particle having a wavefunction [itex]\psi(\vec r, t)[/itex], then:

    [tex]\vec J(\vec r,t)=\frac{\hbar}{2mi}(\psi^* \nabla \psi-\psi\nabla \psi^*)[/tex]

    is the so-called probability current. It represents the flow of probability density, like electrical current is the flow of charge density.
     
  4. May 8, 2005 #3
    Spinor?


    Thanks, Galileo, but I'm trying to "imagine" what is, for example, one of the 2 terms:

    [tex] \psi^* \nabla \psi[/tex]

    Has it any meaning? Is a rotor of the nabla operator?

    :smile:
     
  5. May 8, 2005 #4

    dextercioby

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    Nope,it's just the ~ to the integral nucleus of the momentum operator.

    Daniel.
     
  6. May 8, 2005 #5
    Sorry if this is really basic, i'm no quantum guru yet :tongue:, but could you say that the (classical) velocity is in the direction where [tex]\vec J[/tex] has global max at a given [tex]t[/tex]? Is it possible somehow to calculate [tex]\vec v[/tex] from [tex]\vec J[/tex]?
     
    Last edited: May 8, 2005
  7. May 9, 2005 #6

    dextercioby

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    "(Classical) velocity" has nothing to do with the probability current density...

    Daniel.
     
  8. May 9, 2005 #7
    empirical

    empirical experiments verify this formulae is ok?
     
  9. May 9, 2005 #8

    dextercioby

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    Which formulae...?We can't measure [itex] \vec{j}\left(\vec{r},t\right) [/itex],but only probabilities.

    Daniel.
     
  10. May 9, 2005 #9
    Chr

    Daniel,

    I mean that if exists any experiment or example in real word that confirms that formula or some of its components. For example, if the probability to find a particle in some place or time has this formula...
     
  11. May 9, 2005 #10

    dextercioby

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    I'm not an experimentalist and never will be,but i can assure that this simple part of QM has been fully checked and confirmed.We can't measure certain abstract things.Since QM is a probabilistic theory,all we can do is statistics.

    Daniel.
     
  12. May 9, 2005 #11
    tks Daniel.
     
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