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Simplify laplace-ian problem

  • Thread starter Raparicio
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  • #1
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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
 

Answers and Replies

  • #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.
 
  • #3
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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]
 
  • #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...
 
  • #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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