Where Can I Find a Proof for the Wronskian Formula?

[zaybu]

Can anyone point to a proof for the Wronskian formula:

W[v,v*] = v'v* - vv*' = 2iIM(v', v*)

Thanks

 

[HallsofIvy]

What do you mean by 'IM(v', v*)'?

 

[ChrisVer]

$W= s z^{*}- s^{*}z$
$s=a+ib$
$z=c+id$

$W= (a+ib) (c-id) - (a-ib) (c+id)$
$W= ac -i ad +i bc -bd - ac -i ad +ibc+bd$
$W= -i ad +i bc -i ad +ibc$
$W= 2i bc - 2i ad = 2i (bc-ad)$

$sz^{*} = ac + bd + i (bc-ad)$
so
$Im(sz^{*})= bc-ad$

The proof is already seen

 

[zaybu]

Thanks