关上灯都一样

作者: 日期: 2014/12/29 没有评论

怎么会突然冒出来的呢，因为在颓废了一天之后闲逛网页的时候发现这个站的最后一篇文章竟是一年前的。整个2014年都没有一篇文章不免略显尴尬。好像白交钱供着以往的旧品一样，失去了存在的意义。因为旧品在哪都能供，死了的都要入土，除了那些花大价钱留在水晶棺材里的。我们这种旧品显然不值得受这样的待遇。所以既然还给着钱，就要做点事。哪怕撒野也好，反正是自己的地盘。

于是就来写了。要写什么也不知道。突然要写，却不知道写什么。这样的情况以前也是有的。然而以前总能写下去。现在却非要凭着点什么我怎么也要写点东西出来的感觉才能写了。相比以前，现在连凭空写点什么乱七八糟的都不太提得起兴趣了。写着写着总要泄气，然后就割弃了。上学的时候总还喜欢写。因为那时候总还需要天天握着笔。在语文课本上写的最多。突然想到什么就在课本旁边空白处写起来。当然语文课本上的再多也多不过历史政治课本上的。因为那些是老师强行让你写到空白处[......]

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Quantum Mechanics for Scientists and Engineers Notes 7

作者: 日期: 2013/11/14 2 条评论

1. Angular Momentum

1.1. Angular momentum operators

We will have operators corresponding to angular momentum about different orthogonal axes {\hat{L}_{x}}, {\hat{L}_{y}}, and {\hat{L}_{z}} though they will not commute with each other, in contrast to the linear momentum operator {\hat{p}_{x}}, {\hat{p}_{y}} and {\hat{p}_{z}} which do c[......]

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Quantum Mechanics for Scientists and Engineers Notes 6

作者: 日期: 2013/11/01 6 条评论

1. Types of Linear Operators

1.1. Bilinear expansion of operators

We know that we can expand functions in a basis set as in {f(x)=\sum_{n}c_{n}\psi_{n}(x)} or {|f(x)\rangle=\sum_{n}c_{n}|\psi_{n}(x)\rangle}. What is the equivalent expansion for an operator? We can deduce this from our matrix representation.

Consider an arbitrary function {f}, wri[......]

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Quantum Mechanics for Scientists and Engineers Notes 5

作者: 日期: 2013/10/27 2 条评论

1. Uncertainty Principle and Particle Current

1.1. Momentum, position, and the uncertainty principle

For momentum, we write an operator {\hat{p}}. We postulate this can be written as

\displaystyle \hat{p}\equiv-i\hbar\nabla


with $$! \displaystyle \nabla\equiv\vec{x}_{o}\frac{\partial}{\partial x}+\vec{y}_{o}\frac{\partial}{\partial y}+\vec{y}_{o}\fra[......]

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Quantum Mechanics for Scientists and Engineers Notes 4

作者: 日期: 2013/10/23 1 条评论

1. Time Evolution

1.1. Superposition for particle in a box

Suppose we have an infinitely deep potential well with the particle in a linear superposition, for example, with equal parts of the first and second states of the well (This superposition is normalized) $$! \displaystyle \Psi(z,t)=\frac{1}{\sqrt{L_{z}}}\left[\exp\left(-i\frac{E_{1}}{\hbar}t\right)\sin\left[......]

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Quantum Mechanics for Scientists and Engineers Notes 3

作者: 日期: 2013/10/17 没有评论

1. Particles and Barriers

1.1. Sets of functions

Suppose we are interested in the behavior of some function, such as a loudspeaker cone displacement from time 0 to {t_{o}}, presuming it starts and ends at 0 displacement. An appropriate Fourier series would be

\displaystyle f(t)=\sum_{n=1}^{\infty}a_{n}\sin\left(\frac{n\pi t}{t_{o}}\right)


where $$ {a[......]

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Quantum Mechanics for Scientists and Engineers Notes 2

作者: 日期: 2013/10/07 2 条评论

1. Wave Propagation

1.1. Plane waves and interference

Generalizing to 3 dimensions, the wave equation becomes

\displaystyle \nabla^{2}\phi-\frac{1}{c^{2}}\frac{\partial^{2}\phi}{\partial t^{2}}=0


where

\displaystyle \nabla^{2}\equiv \frac{\partial^{2}}{\partial x^{2}}+\frac{\partial^{2}}{\partial y^{2}}+\frac{\partial^{2}}{\partial z^{2}}


or[......]

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Quantum Mechanics for Scientists and Engineers Notes 1

作者: 日期: 2013/10/03 2 条评论

1. Background Mathematics Review

1.1. Symbols, Greek letters, algebra notations, functions

Relational symbols

  • {\equiv}: "is equivalent to"
  • {\simeq} or {\cong}: "is approximately equal to"
  • {\propto}: "is proportional to"
  • {\gg}: "is much greater than"
  • {\ll}: "is much less than"

Greek letters (Every Greek letter h[......]

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Cryptography I Notes: Stream Cipher

作者: 日期: 2013/09/20 没有评论

This post is my self-notes on Cryptography I (Coursera). The course is taught by Dan Boneh from Standford University. This is only a preliminary review of what I learned from first week. I will update the contents if I got time.

Definition 1 (Symmetric Cipher) A cipher defined over {(\mathcal{K}, \mathcal{M}, \mathcal{C})}, is a pair of "efficient" algorithms $$ {(\mathbf{E},\mathbf{D[......]

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