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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.
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