Fourier Series for the Ground State of a Particle-in-a-Box.

• Oscillations and Waves 2023 Treat the ground state of a quantum particle-in-a-box as a periodic function.

  1. Set up the integrals for the Fourier series for this state.

  2. Which terms will have the largest coefficients? Explain briefly.

  3. Are there any coefficients that you know will be zero? Explain briefly.

  4. Using the technology of your choice or by hand, calculate the four largest coefficients. With screen shots or otherwise, show your work.

  5. Using the technology of your choice, plot the ground state and your approximation on the same axes.