Homework #6

Due Friday of Week 7 at 5pm.

Functions on the complex plane

1. Butkov 2.34 a) - f)

Purpose of question: You already have good intuition about functions of a single real variable, for example, you know the function 1/x blows up at x = 0 and exp(x) blows up as x → ∞. It takes some practice to develop a similar intuition for functions of a single complex variable. The Argand plane can be a minefield of singularities/divergences.

Fourier Series

2. Butkov 4.3

3. Butkov 4.4

4. Butkov 4.12

Fourier Transforms

5. Find the Fourier transform representation of 1/(x^4 + a^4) and show that ΔxΔk satisfies the “uncertainty principle for a wavepacket”. It is not necessary to calculate Δx and Δk precisely, you can use an approximation such as full-width at half max.