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Probability current density

  1. Sep 16, 2007 #1
    Hi folks!

    Can someone tell me how to solve the following... I'd really appreciate it.

    1. The problem statement, all variables and given/known data

    Show that the below two expressions for probability current density are equivalent.

    j(r,t) = h'/2im([tex]\Psi^{*}[/tex][tex]\Delta\Psi[/tex]- ([tex]\Delta\Psi^{*}[/tex])[tex]\Psi[/tex]]

    j(r,t) = real part of [[tex]\Psi^{*}[/tex] (h'/im) [tex]\Delta\Psi[/tex]]


    2. Relevant equations
    h' is the reduced plancks constant h/2pi


    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 16, 2007 #2

    Dick

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    Science Advisor
    Homework Helper

    You should really give us your thoughts (or at least a guess) on this. But if c is a complex number, what's the relation between Im(c) and Re(c/i)? And you may also want to think about integration by parts.
     
  4. Sep 17, 2007 #3
    I'm sorry... but I figured it out. Its a pure math problem. Sometimes my brain just ceases to work!!!

    RP of the second equation is {j(r,t) + [j(r,t)]*}/2 substituting ,we get the first equation.

    Thanks anyways for replying to my post.
     
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