Can the Laplace-ian Problem be Simplified?

[Raparicio]

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

 

[dextercioby]

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.

 

[Raparicio]

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]

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]

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.