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!

Solving a second-order linear ODE in an infinite limit

  1. Sep 18, 2014 #1
    1. The problem statement, all variables and given/known data

    So this is part of a broader problem about the quantum harmonic oscillator, but there's one particular bit of mathematics I'm stuck on.

    We have the differential equation:

    y''(x) +(ε-x2) y = 0

    And I'm told that we're to examine how y behaves as x tends towards infinity. I took this to mean that we can ignore the term in epsilon entirely.

    We're also told that in this limit, we should obtain y = A xk e-x2/2 as the solution to the differential equation.




    2. Relevant equations



    3. The attempt at a solution

    I'm not entirely sure how to go about solving the differential equation (bit rusty) but when I substitute in the given solution, the "xk" term doesn't cancel as I suspect that it should - unless of course you just set k = 0, but the next parts of the question require we prefix it with A x^k . I'm confused.
     
  2. jcsd
  3. Sep 18, 2014 #2

    nrqed

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member


    You should also take the limit in the solution. What is it approximately equal to? Then plugging in the DE will yield a value of k.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Solving a second-order linear ODE in an infinite limit
  1. Second order Linear ODE (Replies: 10)

Loading...