Daily Archives: February 28, 2013

Factors

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因子

factors = independent causes

因素 = 原因元素 = 原因粒子

product = the results of factors multiplying together

產品 = 積 = 因素成果

multiply

乘 = 騎 = 順勢 = 利用

— Me@2013-02-28 8:16 pm

2013.02.28 Thursday (c) All rights reserved by ACHK

微積分 5

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這段改編自 2010 年 6 月 15 日的對話。

導數（derivative）dy/dx 的定義是

   

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{f(x + \Delta x) – f(x)}{(x + \Delta x) – x}

但是，你千萬不要直接背誦這個數式，因為它很繁複。你需要記憶的，是淺白一點的版本：　

   

   

\Delta y = f(x + \Delta x) – f(x)

\frac{dy}{dx} = \lim_{\Delta x \rightarrow 0} \frac{\Delta y}{\Delta x}

— Me@2013.02.28

2013.02.28 Thursday (c) All rights reserved by ACHK

Exchange symmetry

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Because the exchange of two identical particles is mathematically equivalent to the rotation of each particle by 180 degrees (and so to the rotation of one particle’s frame by 360 degrees), the symmetric nature of the wave function depends on the particle’s spin after the rotation operator is applied to it. Integer spin particles do not change the sign of their wave function upon a 360 degree rotation — therefore the sign of the wave function of the entire system does not change. Semi-integer spin particles change the sign of their wave function upon a 360 degree rotation (see more in spin-statistics theorem).

— Wikipedia on Exchange symmetry

2013.02.27 Wednesday ACHK