Homework 1

1) The effect of a nuclear collision between a particle with charge $+e$ and an infinitely massive nucleus of charge $+Ze$, $e$ being the ``proton's'' charge in natural units and $Z$ being the number of protons in the nucleus, is described by the potential energy term:

$$V(r) = \frac{Ze^2}{r}$$

where ${\bf r}$ is the position vector of the particle from the center of force, placed in the origin.

By following the demonstration outlined in class and by using the web notes, demonstrate that the Lenz vector,

$${\bf\epsilon} = -\frac{1}{Ze^2 m} {\bf L} \times {\bf p} + \frac{\bf r}{r}$$

where ${\bf L}$ and ${\bf p}$ are the angular momentum and the momentum of the particle, is a constant of motion.

2) Write down in half a page your thoughts on the importance of Rutherford's type of experiments. What are the most important variables/observables? What is most remarkable in the outcome of the experiment and why?

We will dicuss this again, together in class!