logo

What is Scattering Theory?

What is Scattering Theory?

Explanation1

What is Scattering Theory?

Scattering theory studies the effects that an inhomogeneous medium has on incoming particles or waves. It explains why the sky is blue and Rutherford’s alpha particle scattering experiment, and is also applied in medical imaging technologies such as tomography.

Problems Addressed

Scattering theory can broadly be divided into quantum scattering theory and classical scattering theory. A fundamental problem in classical scattering theory involves “boundaries with impenetrable obstacles” and “media that can be penetrated and have compact support” causing scattering of time-harmonic acoustic/electromagnetic waves.

In scattering theory, the total field uu is divided into the incident field uiu^{i} and the scattered field usu^{s}.

u(x,t)=ui(x,t)+us(x,t) u(x,t) = u^{i}(x,t) + u^{s}(x,t)

To understand, let’s consider a simple example.

1.PNG

In the above situation, ui,usu^{i}, u^{s} are as follows.

ui(x)={axx00x>x0andus(x)={0xx0cx+dx>x0 u^{i}(x) = \begin{cases} a & x \le x_{0} \\ 0 & x \gt x_{0} \end{cases} \quad \text{and} \quad u^{s}(x) = \begin{cases} 0 & x \le x_{0} \\ cx+d & x \gt x_{0} \end{cases}

Then, the total field uu is as follows.

u(x)=ui(x)+us(x)={axx0cx+dx>x0 u(x) = u^{i}(x) + u^{s}(x) = \begin{cases} a & x \le x_{0} \\ cx+d & x \gt x_{0} \end{cases}

See Also


  1. David Colton and Rainer Kress, Inverse Acoustic and Electromagnetic Scattering Theory (4th Edition, 2019), p1 ↩︎