作者superxfq (超級小憤青)
看板Physics
標題Re: [問題] power law potentials
時間Mon Oct 27 23:16:21 2008
I think power law potentials just means the potentials like U(x)=x^n,
and n is a real number.
※ 引述《harry901 (forcing to A cup)》之銘言：
: 請問什麼是power law potentials?
: 我知道potential energy, U
: i.e., gravitational potential U=U(x)=mgx above the earth ...eq(1)
: spring-mass potential U=U(x)=0.5kx^2 ... eq(2)
: it's well-known that (From wiki)
: Given an arbitrary potential energy function V(x), one can do a Taylor
: expansion in terms of x around an energy minimum (x = x0) to model the
: behavior of small perturbations from equilibrium.
: V(x)=V(x0)+V'(x0)*(x-x0)+0.5V''(x0)*(x-x0)^2+o(3) ... eq(3)
: 但是這個power law potentials, U(x-x0)=a*(x-x0)^b,以x0為零點
: 是如何證明的? 跟Taylor有關係嗎?
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1F：推 harry901:This is my problem as shown in the article, 10/27 23:18
2F：→ harry901:U(x-x0)=a*(x-x0)^b, :) 10/27 23:18
3F：→ harry901:The most problem confusing me is how it comes, 10/27 23:19
4F：→ harry901:I can't find the proof from any reference. 10/27 23:20
5F：推 sukeda:In real world, the potential is not with simple form 10/27 23:35
6F：→ sukeda:such as oscillator potential you mentioned, but with 10/27 23:37
7F：→ sukeda:complex form. Hence, we expand the complex potential by 10/27 23:39
8F：→ sukeda:Taylor series which is a good approach. 10/27 23:43