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I Question about solution to Laplacian in Spherical Polars

  1. Mar 31, 2016 #1
    1z3nkua.png
    I was following this derivation of the solution to the Laplacian in spherical polars. I was wondering where the two equations ##\lambda_{1} + \lambda_{2} = -1## and ##\lambda_{1}\lambda_{2} = -\lambda## come from? Thanks.
     
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  3. Mar 31, 2016 #2

    ShayanJ

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    We want to solve the equation ## \frac{d^2S}{dt^2}+\frac{dS}{dt}-\lambda S=0 ##. So let's try a solution of the form ## S=e^{bt} ## (and find b), which gives ## b^2+b-\lambda=0 ##. But for any quadratic equation ## px^2+qx+r=0 ##, we know that the two roots satisfy ## x_1+x_2=-\frac{q}{p} ## and ##x_1x_2=\frac{r}{p}##.
     
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