 Home

Codex Wiki

List of universities

University of Cambridge

Course of the University of Cambridge

Natural sciences course of the University of Cambridge

Year of the natural sciences course of the University of Cambridge

Year 3 of the natural sciences course of the University of Cambridge

Physics course of the year 3 of the natural sciences course of the University of Cambridge

Theoretical Physics course of the University of Cambridge

Theoretical Physics II course of the University of Cambridge

Past exam of the theoretical physics II course of the University of Cambridge

2017

The incident <plane wave> carries <probability current> $j_{\rm in}=\hbar k/m$. For the separated outgoing wave from the previous part,
$$
j_r^{\rm sc}=\frac\hbar m\operatorname{Im}(\psi_{\rm sc}^*\partial_r\psi_{\rm sc})
\sim\frac\hbar{mr}|f(\theta)|^2.
$$
The rate through a distant arc is $rj_r^{\rm sc}\,d\theta$. Dividing by incident flux defines the differential two-dimensional <scattering cross-section>,
$$
\boxed{\frac{d\lambda}{d\theta}=\frac{|f(\theta)|^2}{k},\qquad
\lambda=\frac1k\int_0^{2\pi}|f(\theta)|^2\,d\theta.}
$$
Because $f$ is <dimensionless>, $\lambda$ has units of length, as appropriate for scattering in a plane.

Solution

Past exam of the theoretical physics II course of the University of Cambridge / 2017 / 4 / b / Solution

Past exam of the theoretical physics II course of the University of Cambridge / 2017 / 4 / b / Solution

 Ancestors (14)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the theoretical physics II course of the University of Cambridge / 2017 / 4 / b / Solution

 Ancestors (14)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)