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: Variational Principle

  1. Mar 3, 2008 #1
    1. The problem statement, all variables and given/known data
    If I'm given a potential say A(x/a-m) m an integer, (this is the sawtooth wave)
    What kind of trial function should I use to approximate this?

    2. Relevant equations

    3. The attempt at a solution

    I do recall this function arising in Fourier series. Should I actually solve for the Fourier coefficients to get a trig function? Maybe I'm making this more complicated, is there a simpler way to do this?
  2. jcsd
  3. Mar 4, 2008 #2
    Sorry, I don't really understand what the question. Is this a quantum mechanics problem -- i.e. find an estimate of the ground state and its energy using the variational method?
  4. Mar 4, 2008 #3
    Yes my bad.
  5. Mar 5, 2008 #4
    If you have a periodic potential, it means sense to choose a periodic trial wavefunction. Try using a linear combination of sin and cos at the periodicity of the potential, and use variational methods to find the coefficients.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook