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!

Hermite Polynomials As Part of the Solution to the Harmonic Oscillator

  1. Feb 7, 2009 #1
    1. The problem statement, all variables and given/known data

    When trying to generate solutions to the harmonic oscillator, I'm trying to use hermite polynomials. I understand that there's a recursive relationship between the hermite polynomials but I'm confused in how each hermite polynomial is generated.

    2. Relevant equations
    Hn+1(p)=2*p*Hn(p)-2n*Hn-1(p) to generate each hermite polynomial
    An+1,k = 2An,k-1 -2*n*an-1,k the formula for the coefficients of the hermite polynomials

    3. The attempt at a solution

    The solutions to the harmonic oscillator's energy levels are a combination of hermite polynomials*gaussian functions*normalization constant

    There's a recursive relationship in trying to generate the hermite polynomials but I don't understand how to use the formula for the coefficients of the hermite polynomials. I have that H0=1 and H1=2p as the base cases for the hermite polynomials, but how do I make use of the coefficient formula to generate more hermite polynomials? Can't I just use recursive relationships and have H2 for example depend on H0 and H1? Also, I've read that there are odd and even solutions for hermite polynomials but I don't see how odd n values and even n values have to be treated separately.

  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted