1. Not finding help here? Sign up for a free 30min 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!

Trouble with a 2nd Order D.E.

  1. Oct 10, 2009 #1
    1. The problem statement, all variables and given/known data

    [tex] \frac{d^2\phi(\eta)}{d\eta^2} = (\eta^2 - K) \phi(\eta) [/tex]

    Where K is essentially a constant, K = 2n + 1 (n is an integer).


    3. The attempt at a solution

    I don't even know where to begin since [tex]\phi[/tex] is a function of [tex]\eta[/tex]. A push in the right direction would be much appreciated.
     
  2. jcsd
  3. Oct 10, 2009 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    Stuff that looks like that usually wind up having solutions that are special functions (like Bessel etc). That appears to be a parabolic cylinder function. I got that by creative googling. It may have a simpler form for the case K = 2n + 1. Don't know. But that will give you a start for researching it. What kind of course is this? Are you supposed to be able solve it simply?
     
  4. Oct 11, 2009 #3
    Thanks for the reply. This is for my quantum mechanics course, and the equation I set up relates to solving the time-independent Schrodinger equation for the harmonic oscillator in momentum-space. My textbook solved a similar DE using Hermite polynomials, but I was hoping there was a simpler solution. I'll search for special functions & "parabolic cylinder function." Thanks again for the reply.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Trouble with a 2nd Order D.E.
  1. 2nd Order D.E. help (Replies: 5)

  2. 2nd order d.e (Replies: 2)

Loading...