- #1

touqra

- 287

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I don't know where have I gone wrong...

I converted Cartesian coordinates to polar coordinates:

[tex] \frac{\partial^2\Psi}{\partial x^2} +\frac{\partial^2\Psi}{\partial y^2}= \frac{1}{2}(\frac{\partial^2}{\partial x^2}+\frac{\partial^2 }{\partial y^2})\Psi^2 - \Psi(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2})\Psi

=\frac{\partial^2\Psi}{\partial r^2}+ \frac{1}{r^2}\frac{\partial^2\Psi}{\partial \Phi^2}[/tex]

But on the left hand side (the Cartesian components) is just the Laplacian in 2D, but the final answer I got for the polar components is not equivalent to the Laplacian for polar coordinate system.

I'm missing the term [tex]\frac{1}{r}\frac{\partial\Psi}{\partial r}[/tex]

I converted Cartesian coordinates to polar coordinates:

[tex] \frac{\partial^2\Psi}{\partial x^2} +\frac{\partial^2\Psi}{\partial y^2}= \frac{1}{2}(\frac{\partial^2}{\partial x^2}+\frac{\partial^2 }{\partial y^2})\Psi^2 - \Psi(\frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2})\Psi

=\frac{\partial^2\Psi}{\partial r^2}+ \frac{1}{r^2}\frac{\partial^2\Psi}{\partial \Phi^2}[/tex]

But on the left hand side (the Cartesian components) is just the Laplacian in 2D, but the final answer I got for the polar components is not equivalent to the Laplacian for polar coordinate system.

I'm missing the term [tex]\frac{1}{r}\frac{\partial\Psi}{\partial r}[/tex]

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