Re: [問題] 雙體質心動量的問題
※ 引述《KaryuuIssen (FIRE DRIFT)》之銘言：
: 假設質點m1和m2的動量分別是p1和p2
: 我們知道能量 E = (p1)^2/2m1 + (p2)^2/2m2
: 然而上式可以改寫成
: E = Ｐ^2/2Ｍ + ｐ^2/2ｍ
: 其中Ｐ = p1 + p2
: ｐ = (m2p1-m1p2)/(m1+m2)
: Ｍ = m1 + m2
: ｍ = m1m2/(m1+m2)
: 改寫後是把質心當作慣性座標系嗎？
: 上面的關係式我實在不能解讀他的物理意義....
: 重點是從量力的角度來看
: E、ｐ、Ｐ、Ｒ好像有哪些會commute？
: 其中Ｒ = (m1r1+m2r2)/(m1+m2)
: 這部份我不確定，只是印象中今天課堂上有提到...
: 感謝解惑orz
I believe that the first term refers to the energy associates with
the "Center of Mass" and the second term refers to the energy of
" motion relative to the Center of Mass." If you are asking what's
the physical meaning of this, I personal think it just easy to do
the calculation. For example, in classical mechanics, we can write
down the lagrangian for the motion and break up in to equation of motion
that refers to CM and the relative motion. And this is much simpler
than just calculating two individual objects since most of the time
when you are dealing system with 2 objects, you need to solve the EoMs
as a system. However, if you turn that into CM and relative motion, most
of the time you are just solving two individual EoMs (like 2 ODEs).
Another point of view, as you said is about QM. An example I can think of
is the hydrogen atom. When we are dealing with schrodinger's equation
it's more complicated to write 1 schrodinger equation with 2 particles, so
the way to reduce the complication is the transfer two particles into a
system that refers to CM and reduced mass. (Im not saying you cant do the
schrodinger with 2 particles,its just as a physicsit, people always try to
go with a easier way.)
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※ 編輯: lewisweilin 來自: 99.245.10.248 (03/27 13:50)
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