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