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Series expansion

  1. Apr 19, 2007 #1

    quasar987

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    1. The problem statement, all variables and given/known data
    I am ashamed to ask this, but in my quantum final, there was a little mathematically-oriented subquestion that asked to show that the function

    [tex]V(r)=-\frac{V_0}{1+e^{(r-R)/a}}[/tex]

    (r in [0,infty)) can be written for r>R as

    [tex]V_0\sum_{n=1}^{\infty}(-1)^ne^{-n(r-R)/a}[/tex]


    3. The attempt at a solution
    :blushing:
     
  2. jcsd
  3. Apr 19, 2007 #2

    matt grime

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    You know the series expansion of (1+x)^-1 for |x|<1, right? So use it (and don't tell me that exp{(r-R)/a} >1 for r>R, because I know that).
     
  4. Apr 19, 2007 #3

    quasar987

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    Yeah ok!

    ----
     
  5. Apr 19, 2007 #4

    HallsofIvy

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    Or (really the same thing) the "geometric series"
    [tex]\sum_{n=0}^\infty ar^n= \frac{a}{1- r}[/tex]
     
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