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Wronskian formula

  1. Jun 6, 2014 #1
    Can anyone point to a proof for the Wronskian formula:

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

    Thanks
     
  2. jcsd
  3. Jun 6, 2014 #2

    HallsofIvy

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    What do you mean by 'IM(v', v*)'?
     
  4. Jun 7, 2014 #3

    ChrisVer

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    [itex] W= s z^{*}- s^{*}z[/itex]
    [itex]s=a+ib[/itex]
    [itex]z=c+id[/itex]

    [itex] W= (a+ib) (c-id) - (a-ib) (c+id)[/itex]
    [itex] W= ac -i ad +i bc -bd - ac -i ad +ibc+bd[/itex]
    [itex] W= -i ad +i bc -i ad +ibc[/itex]
    [itex] W= 2i bc - 2i ad = 2i (bc-ad)[/itex]

    [itex] sz^{*} = ac + bd + i (bc-ad) [/itex]
    so
    [itex] Im(sz^{*})= bc-ad[/itex]

    The proof is already seen
     
  5. Jun 9, 2014 #4
    Thanks
     
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