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I Sturm-Liouville Problem, boundary condition

  1. Mar 28, 2016 #1
    46843bd5250780c5b80f9ce7cedb4a94.png

    given the generalized SL conditions

    260895bbe02b9032a667ce60edb101dd.png
    10259e92b5c3019525bafbb12ef45065.png


    diff87.png

    Let's say psi_m and psi_n are eigenfunctions of the given y.
    Its Wronskian is 0 because otherwise the boundary condition doesn't make sense much.

    However, I wonder if it is possible to have,



    S={ x | W[psi_m(x) , psi_n(x)] =/= 0 }
    otherwise W[psi_m(x) , psi_n(x)] = 0



    then alpha and alpha' are 0 at such points, but still satisfies SL conditions.
    Would it matter because at those points we can have any psi_m(x) and psi_n(x)?

    If not could anyone tell me why?
     
  2. jcsd
  3. Mar 29, 2016 #2
    ah, forgot to mention that, alpha' = alpha_2. whereas alpha = alpha_1

    I could not find the equation picture of SL conditions of wronskian using psi_m, psi_n and alpha and alpha'.
     
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