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 Exercise [10.11] 
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Joined: 12 Mar 2008, 10:57
Posts: 69
Location: India
Post Exercise [10.11]
\frac{\partial{\phi}}{\partial{\overline{z}}}=0
\Rightarrow\ \frac{\partial{x}}{\partial{\overline{z}}}\frac{\partial{\phi}}{\partial{x}}+ \frac{\partial{y}}{\partial{\overline{z}}}\frac{\partial{\phi}}{\partial{y}}=0
\Rightarrow\ \frac{1}{2}(\frac{\partial{(z+\overline{z})}}{\partial{\overline{z}}}\frac{\partial{\phi}}{\partial{x}}+ \frac{\partial{(z-\overline{z})}}{\partial{\overline{z}}}\frac{\partial{\phi}}{\partial{y}})=0
\Rightarrow\ \frac{\partial{\phi}}{\partial{x}}-1/i(\frac{\partial{\phi}}{\partial{y}})=0
\Rightarrow\ \frac{\partial{\phi}}{\partial{x}}+i(\frac{\partial{\phi}}{\partial{y}})=0


23 May 2008, 12:20

Joined: 07 May 2009, 16:45
Posts: 62
Post Re: Exercise [10.11]
You are missing a "1/i" in the third line of the proof. From the substitution y = (z-z*)/2i


07 Jul 2009, 20:39
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