球协函数图像的绘制

本文利用 Python 编程语言实现归一化球协函数图像的数据准备,并用 Mathematica 绘制图像。

归一化球协函数为:

 Y_{lm}(\theta,\phi)=\sqrt{\frac{2l+1}{4\pi}\frac{(l-m)!}{(l+m)!}}P_l^m(\cos(\theta))e^{im\phi}

其中 l=0,1,2,\cdots,m=0,\pm 1,\pm 2, \cdots, \pm l,\quad P_l^m(\cos \theta) 为连带勒让德函数

m>0 时,把 m 递归到零:

\sqrt{1-x^2}P_l^m(x)=\frac{1}{2l+1}[(l-m+1)(l-m+2)P_{l+1}^{m-1}(x)-(l+m-1)(l+m)P_{l-1}^{m-1}(x)]

m<0 时,把 m 递归的零:

\sqrt{1-x^2}P_l^m(x)=\frac{1}{2l+1}[P_{l-1}^{m+1}(x)-P_{l+1}^{m+1}(x)]

m=0 时,把 l 递归到零:

(l-m)P_l^m(x)=(2l-1)xP_{l-1}^m(x)-(l+m-1)P_{l-2}^m(x)

利用以上三式就可以通过递归程序定义连带勒让德函数。

下面是 Python 程序代码

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Mathematica 相关 — 鲁大科协

1、Mathematica 历史和背景

http://www.wolfram.com/company/background.html

http://www.wolfram.com/mathematica/quick-revision-history.html

2、Mathematica 下载、安装与破解方法,学习及使用

http://subs.zhli.net/mathematica-download/

3、Mathematica 语言介绍

下载:
pdfMathematica 语言介绍.pdf [201.09 kB] -

4、利用Mathematica编制光斑位移自动化测量程序

下载:
CDF版: cdf利用Mathematica编制光斑位移自动化测量程序.cdf [942.18 kB] - 需要用 Mathematica 打开
PDF版: pdf利用Mathematica编制光斑位移自动化测量程序.pdf [1.16 MB] - -

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Emacs for Windows

下载地址:
http://ftp.gnu.org/gnu/emacs/windows

简单配置:

;;My Options
(setq inhibit-startup-message t)
(global-linum-mode t)
(column-number-mode t)
(setq scroll-margin 3
      scroll-conservatively 10000)
(setq default-major-mode 'text-mode)
(mouse-avoidance-mode 'animate)
(setq frame-title-format "emacs@%b")
(auto-image-file-mode)
(setq make-backup-files nil)
(setq delete-auto-save-files t)

(tool-bar-mode 0)
;(menu-bar-mode 0)
;(scroll-bar-mode 0)

(global-set-key (kbd "RET") 'newline-and-indent)

(setq c-default-style "stroustrup")
(setq c++-default-style "stroustrup")

(setq indent-tabs-mode nil)
(setq default-tab-width 4)
(setq tab-width 4)
(setq tab-stop-list ())
(setq tab-stop-list '(4 8 12 16 20 24 28 32 36 40
                    44 48 52 56 60 64 68 72 76 80 84 88 92 96))

(display-time-mode 1)                
(setq display-time-24hr-format t)
(setq display-time-day-and-date t)

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Steve Jobs 在2005年斯坦福大学毕业典礼的演讲

"Stay Hungry, Stay Foolish." 求知若饥,虚心若愚

2 June 2005, Palo Alto, CA

音频片段:需要 Adobe Flash Player(9 或以上版本)播放音频片段。 点击这里下载最新版本。您需要开启浏览器的 JavaScript 支持。

Thank you.

I'm honored to be with you today for your commencement from one of the finest universities in the world. Truth be told, I never graduated from college, and this is the closest I've ever gotten to a college graduation. Today, I want to tell you three stories from my life. That's it. No big deal. Just three stories.

The first story is about connecting the dots. I dropped out of Reed College after the first six months, but then stayed around as a drop-in for another 18 months or so before I really quit. So why did I drop out?

It started before I was born. My biological mother was a young, unwed graduate student, and she decided to put me up for adoption. She felt very strongly that I should be adopted by college graduates, so everything was all set for me to be adopted at birth by a lawyer and his wife -- except that when I popped out they decided at the last minute that they really wanted a girl.

So my parents, who were on a waiting list, got a call in the middle of the night asking, "We've got an unexpected baby boy; do you want him?" They said, "Of course." My biological mother found out later that my mother had never graduated from college and that my father had never graduated from high school. She refused to sign the final adoption papers. She only relented a few months later when my parents promised that I would go to college. This was the start in my life.

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《世界是平的》——摘录

Thomas L. Friedman.The World Is Flat.2005

1、在非洲,瞪羚每天早上醒来时,它知道自己必须跑得比最快的狮子还快,否则就会被吃掉。狮子每天早上醒来时,它知道自己必须超过跑得最快的瞪羚,否则就会被饿死。不管你是狮子还是瞪羚,当太阳升起时,你最好开始奔跑

2、在三重汇合的作用下,这个全新的平坦世界平台,已经开始摧毁我们的围墙、天花板和地板。也就是说,世界通过光缆、互联网和工作流软件等的联结,已经摧毁了妨碍合作的围墙。人们从来没有想到他们能一起工作,人们从来没有想到工作会在国家之间流动,现在很多传统的高墙已经消失了。相同的平台也已经掀去了我们的天花板。人们从来没有想到能够把他们的意见上传到博客,式者上传上传一种新的政治视野,或者上传一部百科全书,或者上传一种新的软件。人们突然发现,作为个体,他们能够对世界产生全球冲击。随着天花板的消失,人们就能够向上突破,以之前想象不到的方式获成功。接着,地板最后也消失了。由于搜索行业的兴起,人们能够寻根究底,搜索到事实、引文、历史,以及从未谋面的陌生人的个人数据。阻碍我们深入挖掘过去或现在任何事物或任何人的传统的坚硬的水泥地板已经消失了。

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