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## Main Question or Discussion Point

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.

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!

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!