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In my book it says that the schrodinger equation,

[tex]

i\hbar\frac{\partial\Psi}{\partial t} = \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi

[/tex]

rearranged is,

[tex]

\frac{\partial\Psi}{\partial t} = \frac{i\hbar}{2m}\frac{\partial\Psi ^2 psi}{\partial x^2} - \frac{i}{\hbar}V\Psi

[/tex]

how does the complex number, move over, and in the numerator? instead of the denominatior?

I can see how [tex] A\hbar = B\hbar ^2 becomes A = B \hbar [/tex]

but I don't understand how

[tex] A i = B + V\Psi becomes A = iB - i V\hbar [/tex]

could someone please explain to me the mathematical rules behind rearranging complex numbers in equations,

or give me some links that explain it, (in simple terms) please :P