Central Forces: Spring-2026
HW 01: Due W1 D3: Math Bits

1. Syllabus and Schedule

   Find the course syllabus and schedule on Canvas. Read through them carefully and bring your questions to the second day of class.

2. Compare Fourier Series to Particle-in-a-Box Consider the function: \begin{equation*} f(x)=\begin{cases} 0&0<x<\frac{L}{3}\\ D & \frac{L}{3}<x<\frac{2L}{3}\\ 0&\frac{2L}{3}<x<L \end{cases} \end{equation*}

   1. You can think of this function as periodic, with period \(L\). Expand this function in a Fourier series.

      Plot an approximation containing eight nonzero terms.

      Make a histogram of your coefficients. Be thoughtful about the horizontal axis of your histogram.

   2. Extra Credit Challenge You can also think of this function as representing a quantum particle in a box of size \(L\). Expand this function in quantum particle in a box energy eigenstates.

      Plot an approximation containing eight nonzero terms.

      Make a histogram of your coefficients. Be thoughtful about the horizontal axis of your histogram.

   3. Extra Credit Challenge: Briefly reflect on the similarities and differences between the previous two cases. You may find it interesting to plot your approximations from \(x=-2L\) to \(x=2L\)