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Help to explain expansion

  1. Jul 25, 2013 #1
    Hi,

    Could you help me to understand the following expansion I found in a book of qunatum mechanics.

    |1+a|^2=1+a+a*+... where a* is the complex conjugate of a
     
  2. jcsd
  3. Jul 25, 2013 #2

    hilbert2

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    What are the remaining terms in the expansion? I don't think it is an infinite series...

    If ##a=x+iy##, where ##x## and ##y## are real, then we have

    [itex]\left| 1+a \right|^{2} = (1+a)(1+a)^{*}=(1+x+iy)(1+x-iy)=1+x+x^{2}+y^{2}=1+\frac{a}{2}+\frac{a^{*}}{2}+a^{*}a[/itex]
     
  4. Jul 25, 2013 #3

    micromass

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    I really don't see how you got this. To me it's

    [tex]|1 + a|^2 = (1+a)(1+a)^* = (1 + a)(1 + a^*) = 1 + a + a^* + aa^*[/tex]
     
  5. Jul 25, 2013 #4

    hilbert2

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    ^ Sorry, it should have been ##1+2x+x^{2}+y^{2}##. :blushing:
     
  6. Jul 25, 2013 #5

    This expansion has errors...
    If ##a=x+iy##, where ##x## and ##y## are real, then we have

    [itex]\left| 1+a \right|^{2} = (1+a)(1+a)^{*}=(1+x+iy)(1+x-iy)=(1+x)^2+y^2=x^2+2x+1+y^2=1+x+iy+x-iy+(x+iy)(x-iy)=1+a+a{*}+(a)(a){*}[/itex]
    Hope this helps...
     
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