Hi guys, I got a question in the solid state physics book writen by ashcroft and mermin. This question is about the relationship between momentum and force.(adsbygoogle = window.adsbygoogle || []).push({});

Suppose we have an electron with momentum p(t) at time t. If there is a force f(t) acted on this electron in the ongoing infinitesimal time dt, its momentum will change to p(t+dt) at time t+dt.

The book says that, p(t+dt)=p(t)+f(t)dt+O(dt)~2 where O(dt)~2 denotes a term of the order of (dt)~2.

I don't know why there is a term O(dt)~2 ?

According to dp/dt=f(t) we have dp=f(t)dt+a(dt) where a(dt) means a higher order term of dt. But why is this high order term is the term of the order of (dt)~2 instead of 3, 4...

Can you help me about this question, I will show you the snapshot of the book in the next floor, thank you!

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# A question about the relationship between momentum and force

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