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Solving a time independent Schrodinger equation

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data
    Hello!
    I am currently stuck with a time independent Schrodinger equation where the potential "V(x)" is hyperbolic in nature. I was wondering if any one could give me a hint as to how I should approach this problem in order to get an analytical solution (without using numerical techniques).



    2. Relevant equations
    The equation is of the form,
    d²/dx²(Ѱ) + 2m/ħ²{E + δp²/x(p-x)}(Ѱ) = 0
    where the voltage V(x) = -{δp²/x(p-x)}


    3. The attempt at a solution
    Thank you!
     
  2. jcsd
  3. Apr 7, 2012 #2
    Stupid question: is [itex]\delta[/itex] just a number here?
     
  4. Apr 7, 2012 #3
    Yes, δ, E, p are all constants.
    I am trying to solve it by defining z = y(x) and changing the differential equation. But it is getting quite complicated. :(

    Any help would be gladly appreciated.
     
  5. Apr 8, 2012 #4
    Did u try series solution for diffrntial eqn
     
  6. Apr 8, 2012 #5
    Yes. But I am unable to reduce the equation to any of the forms I know (bessel, legendre, laguerre, hermite, chebyshev).
     
  7. Apr 8, 2012 #6
    I believe the solution is a series, I'll give you a clue; hyper
     
  8. Apr 9, 2012 #7
    Yesss!!! Thank you!!! I believe it can be reduced to the hypergeometric form. Thank you very much [bold]genericusrnme[/bold] !!
    I will post the solution as soon as I finish.
     
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