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Simplify laplace-ian problem

  1. Jan 24, 2005 #1
    Dear Friends,

    I have this problem:

    [tex] \frac{i\hbar\Psi}{2m}\frac{\partial\nabla\Psi}{\partial t}+(\frac{i\hbar(\nabla\Psi)}{2m}\nabla)\frac{i\hbar(\nabla\Psi)}{2m}[/tex]

    ... and i'd like to simplify it... is is possible?

    best reggards
     
  2. jcsd
  3. Jan 24, 2005 #2

    dextercioby

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    The only way i can see it,u may write the laplace-ian in the second term.I assume [itex] \Psi [/itex] to be scalar,hence nabla apllied on it would be the gradient and another nabla would mean laplace-ian...It could mean hessian,but i doubt it is the case here...

    Daniel.
     
  4. Jan 25, 2005 #3
    Like this?

    want you mean this?

    [tex] \frac{i\hbar\Psi}{2m}\frac{\partial\nabla\Psi}{\partial t}+(\frac{i\hbar(\nabla^2\Psi)}{2m})\frac{i\hbar(\nabla\Psi)}{2m}[/tex]
     
  5. Jan 25, 2005 #4

    dextercioby

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    No,i mean this:
    [tex] \frac{i\hbar}{2m}\Psi \frac{\partial}{\partial t}\nabla \Psi+\frac{i\hbar}{2m}(\nabla\Psi)\frac{i\hbar}{2m}\Delta \Psi [/tex]

    Daniel.

    P.S.Nabla is an (differential) linear operator which applies to the right ALWAYS...
     
  6. Jan 25, 2005 #5

    dextercioby

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    Sorry,it's the same thing as you have written,it's just that i thought u applied that nabla to the left (else you would have written like i did,without changing the order of terms),instead of to the right...

    My applogies,if i assumed a wrong thing...

    Daniel.
     
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