Variational Principle: Solving a Sawtooth Wave Potential

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Homework Help Overview

The discussion revolves around a variational principle applied to a sawtooth wave potential in the context of quantum mechanics. Participants are exploring how to select an appropriate trial function for approximating the ground state energy.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to connect the problem to Fourier series and questions whether solving for Fourier coefficients is necessary. Some participants seek clarification on the nature of the problem, specifically if it pertains to estimating ground state energy using variational methods.

Discussion Status

Participants are actively engaging with the problem, with some suggesting the use of periodic trial wavefunctions and variational methods. There is a recognition of the need for a suitable approach, but no consensus has been reached on the specific method to employ.

Contextual Notes

There is some uncertainty regarding the interpretation of the problem and the specifics of the potential involved. The original poster's reference to Fourier series indicates a possible complexity in the approach being considered.

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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?
 
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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?
 
Yes my bad.
 
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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