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I've seen the Schrodinger equation written in the following form:

[tex]i\hbar\frac{\partial\Psi}{{\partial}t} = -\frac{\hbar^2}{2m}\nabla^2\Psi + V\Psi[/tex]

where

[tex]\nabla^{2} = \frac{\partial^{2}}{{\partial}x^2} + \frac{\partial^2}{{\partial}y^2} + \frac{\partial^2}{{\partial}z^2}[/tex]

Now, is [itex]\nabla^2\Psi[/itex] a vector or a scalar? In this notation, I would say it's a vector. You have [itex]\nabla^2[/itex] acting on each of the components of [itex]\Psi[/itex]. However the book seems to say that [itex]\nabla^2\Psi[/itex] is a scalar. Shouldn't the notation then be [itex]\nabla^2\cdot\Psi[/itex]? That is, shouldn't it be a dot product? I'm rather confused...

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# Question on Notation

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