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Quantum scattering theory

  1. Jun 17, 2010 #1
    in Schaum's Outline of Theory and Problems of Quantum Mechanics

    how did they got eq 15.5.7

    qpnns5.jpg
     
  2. jcsd
  3. Jun 17, 2010 #2
    Did you try using the relation

    [tex]\sin[x]=\frac{\exp[ix]-\exp[-ix]}{2i}[/tex]

    in Equation 15.5.6 and expanding to see what you get? It looks like you should get the result they obtain if you work at it using that relation.
     
  4. Jun 18, 2010 #3
    the second eq II ?? it's equale zero why??
     
  5. Jun 18, 2010 #4
    If you have expanded Equation 15.5.6 using the substitution given, try separating the resulting equation into the real and imaginary components. It looks to me like Equation I in 15.5.7 is the imaginary part and Equation II of 15.5.7 is the real part after substituting for [itex]\sin[x][/itex].
     
  6. Jun 18, 2010 #5

    gabbagabbahey

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    I don't think that the two parts of 15.5.7 are the real and imaginary parts of 15.5.6, but rather they result from the fact that [itex]e^{ikr}[/itex] and [itex]e^{-ikr}[/itex] are orthogonal functions of [itex]r[/itex], and hence the relation [tex]\alpha e^{ikr}+\beta e^{-ikr}=0[/itex] can only be true for all [itex]r[/itex] if [itex]\alpha=\beta=0[/itex].
     
  7. Jun 21, 2010 #6
    jdwood983 and gabbagabbahey thanks for help
     
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