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Equation of continuity

  1. Jan 3, 2008 #1
    1. The problem statement, all variables and given/known data

    Use the Schrodinger Equation to show that

    [tex]\frac{\partial}{\partial t}(\Psi^{*} \Psi) = - \underline{\nabla}. \underline{j}[/tex]

    2. Relevant equations

    [tex]\underline{j} = \frac{-i}{2m} \left[\Psi^{*}(\nabla \Psi) - (\nabla \Psi^{*})\Psi]\right[/tex]

    [tex]\frac{\partial}{\partial t}n(x,t) = -\underline{\nabla}. \underline{j}(x,t)[/tex]

    [tex]n(x,t) = \Psi^{*}(x,t)\Psi (x,t)[/tex]

    I'm not sure how the Schrodinger equation comes into play here... can anyone offer any suggestions?
  2. jcsd
  3. Jan 3, 2008 #2


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    Science Advisor
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    On the left hand side I see a time derivative, while on the right hand side there is a space derivative (gradient). The Schrödinger equation contains both, so you could use it to go from one to the other (and you might also want to use the complex conjugate of it)
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