What Are Characteristic Scale Arguments in Physics?

[center o bass]

In physics one often invokes arguments about a characteristic scale. For example at distances much larger than the Compton wavelength (a characteristic length scale) one might ignore quantum phenomena and calculate classically.

I would like to read up some more on the thinking behind such arguments, their validity etc. Does anyone know of some good literature on this topic?

 

[ORF]

Hello

First of all, my mother language is not English, so I'll be glad if you correct any mistake.

The Compton wavelength is a particular case of the "de Broglie length wave" for electrons. The great idea behind this concept is the complementarity principle.

http://en.wikipedia.org/wiki/Complementarity_(physics)

The complementarity in quantum physics could be summarized as "propagating as a wave; interacting with matter as a particle".

When you detect a quanta, you will measure its properties as a particle. When you don't detect a quanta, but its interference with itself, you will measure its properties as a wave, and among other things, its "de Broglie's wavelength".

It's a tricky point, and I think the best introduction is a historical view. I would recommend you The Nobel Lecture of de Broglie. http://www.nobelprize.org/nobel_prizes/physics/laureates/1929/broglie-lecture.pdf. The textbook Eisberg&Resnick, Quantum Physics, which is often used for the first year of quantum physics classes at university, has a nice historical introduction.

And an even deeper text is "The Feynman Lectures on Physics". Vol. 3-4, p. 221-222, 412.

Greetings.
PD: Quantum phenomena are not only related to small sizes; a very graphical example is when you try to measure the temperature of a water droplet with a mercury-in-glass thermometer: this is also quantum physics :)