Variational Principle: Solving a Sawtooth Wave Potential

[Nusc]

Homework Statement

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?

Homework Equations

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?

 

[genneth]

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?

 

[Nusc]

Yes my bad.

 

[genneth]

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.