1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Solving a time independent Schrodinger equation

  1. Mar 31, 2012 #1
    1. The problem statement, all variables and given/known data
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook