# Simplify laplace-ian problem

Dear Friends,

I have this problem:

$$\frac{i\hbar\Psi}{2m}\frac{\partial\nabla\Psi}{\partial t}+(\frac{i\hbar(\nabla\Psi)}{2m}\nabla)\frac{i\hbar(\nabla\Psi)}{2m}$$

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

best reggards

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dextercioby
Homework Helper
The only way i can see it,u may write the laplace-ian in the second term.I assume $\Psi$ 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.

Like this?

want you mean this?

$$\frac{i\hbar\Psi}{2m}\frac{\partial\nabla\Psi}{\partial t}+(\frac{i\hbar(\nabla^2\Psi)}{2m})\frac{i\hbar(\nabla\Psi)}{2m}$$

dextercioby
Homework Helper
No,i mean this:
$$\frac{i\hbar}{2m}\Psi \frac{\partial}{\partial t}\nabla \Psi+\frac{i\hbar}{2m}(\nabla\Psi)\frac{i\hbar}{2m}\Delta \Psi$$

Daniel.

P.S.Nabla is an (differential) linear operator which applies to the right ALWAYS...

dextercioby