哲

Consider a system of three non-interacting identical spin 1/2 particles that are in the same spin up state and confined to moved in a one-dimensional infinite potential well of length a : V(x)=0 for 0<x<a and V(x)=infinite for other value of x.

Determine the energy and wave function of the ground state, the first excited state, and the second excited state.

請試著證明以下的定積分

圖片參考：https://s.yimg.com/rk/AE03766702/o/1214158529.gif

求以下的積分

圖片參考：https://s.yimg.com/rk/AE03766702/o/216255285.gif

其中a , b >=0

Let

圖片參考：https://s.yimg.com/rk/AE03766702/o/17353732.gif

where x,n,a>=0.

Try to prove that F(x,n,a)=x+n+a

A simple pendulum is placed on an elevator which rises upward at an acceleration a as shown in the figure. If the pendulum is displaced at an amount theta from vertical and released from rest relative to the elevator , find the tension T in the supporting light rod when theta=0.

圖片參考：https://s.yimg.com/rk/AE03766702/o/520999212.png

Let G be a set with an operation * such that :

(1)G is closed under *

(2)* is associative

(3)There exists an element e in G such that e*x=x for all x in G

(4)Given x in G, there exists a y in G such that y*x=e

Prove that G is a group.(Thus you must show that x*e=x and x*y=e for e,y above)

Find the area of the surface cut from the hemisphere x^2+y^2+z^2=4 , z>0 , by the cylinder x^2+y^2=2x

試證明

圖片參考：http://latex.codecogs.com/gif.latex?%5cint_{-%5cin...

其中 i 是虛數，k 是一常數

能以複變函數論證明最好

Solve in MATLAB the following eqation

圖片參考：http://latex.codecogs.com/gif.latex?\frac{\mathrm{...

for a few particles starting at different position x and velocity v.

Take Fourier transform of x(t). Plot and compare the Fourier spectrum

for p=0.1 and p=1.0

有個簡單的小實驗是這麼做的:

(1)將鋅粉加入煮沸的氫氧化鈉中

(2)再將一圓銅幣置於熱溶液中3~5分鐘後，銅幣會鍍上一層薄薄的鋅變成銀色銅幣

(3)再將銀色銅幣加熱後銀色銅幣會漸漸變成金色

小弟比較疑惑的是步驟二的原理。

常理上來說鋅的活性相對於銅是比較大

鋅銅電池的原理就是利用鋅和銅的活性的差異

但是我爬文找到步驟二的原理卻是銅還原了鋅

鋅還原銅是自發性反應

但銅還原鋅便不是自發性反應 ，而是非自發性反應了

有可能是因為高溫的溶液提供的熱能驅使非自發性反應發生嗎?

有人可以提供詳細的原理和理由嗎?

現在有三個圓柱:x^2+y^2=1, y^2+z^2=1, z^2+x^2=1

試求被三個圓柱包圍的體積

Please prove that

圖片參考：http://latex.codecogs.com/gif.latex?\frac{x^{2}+y^... e^{x+y-2}

for any x>=0 , y>=0

Please show that

圖片參考：http://latex.codecogs.com/gif.latex?\int_{0}^{\fra... }{6}}\frac{d\theta }{8sin^{2}\theta +1}=\frac{\pi }{9}

A massless rope is tossed over a wooden dowel of radius r in order to lift a

heavy object of weight W off the floor. The coefficient of sliding friction

between the rope and dowel is μ. Show that the minimum downward pull

on the rope necessary to lift the object is

圖片參考：http://latex.codecogs.com/gif.latex?F_{down}=We^{\... \mu }

圖片參考：http://img138.imageshack.us/img138/6045/kjfhg.png

由於剛進大學，

對於計概原文書中的句子意思有些不了解，

因此拜託各位大大幫幫忙解釋了

[1]

Computer science is no more about computers than astronomy is about telescopes, biology is about microscopes, or chemistry is about beakers and test tubes. Science is not about tools. It is about how we use them and what we find out when we do.

請問紅色和藍色about部分的用法和意義是怎麼?

[2]

These packages are widely used by professionals in all fields. However, learning to use a software package is no more a part of computer science than driver's education is a branch of automotive engineering. A wide range of people use computer software, but the computer scientist is responsible for specifying, designing, building, and testing software package as well as the compute the computer systems on which they run.

請問紅色是怎麼意思

麻煩大大分析一下

還有specify是怎麼意思?(查過單字了但不確定)

[Question]

The navigator of an oil tanker uses the satellites of the Global Positioning System (GPS/NAVSTAR) to find latitude and longitude .

These are 43度36分25.3秒N and 77度31分48.2秒W.

If the accuracy of these determination is ±0.5秒 , what is the uncertainty in the tanker's position measured along (a) a north-south line (merdian of longitude) and (b) an east-west line (parallel of latitude)? (c) Where is the tanker?

[Answer]

(a)31m

(b)22m

可以請教過程嗎?還有紅色字體意思是怎麼?

拜託了~~

圖片參考：http://latex.codecogs.com/gif.latex?\int_{0}^{\inf... }e^{-x^{2}}dx

請積分以上的積分式

這只能以無窮小數來表達嗎?

所謂的完美數

就是一個數恰好等於它的因數(小於本身)和

如6的因數有1、2、3(6不算)

而1+2+3洽=6

因此6是完美數

求1000以內所以的完美數的C程式

-----------------------------------------------

#include<stdio.h>

#include<stdlib.h>

int main(void)

{

int i,n,sum=0;

printf("1到1000中所有的完美數有: ");

for(n=2;n<=1000;n++)

{

for(i=1;i<=n-1;i++)

{

if(n%i==0)

sum+=a;

}

if(n=sum)

printf("%d ",n);

}

printf("\n");

system("pause");

return 0;

}

執行後卻發現無法求得完美數

請問各位前輩小弟的程式碼哪裡有問題呢?

拜託了~

麻煩解下面兩題不定積分，並附上過程

[1]

圖片參考：http://img72.imageshack.us/img72/5818/6354961.png

[2]

圖片參考：http://img14.imageshack.us/img14/5818/6354961.png

已知P為質數

試證明：

(P-1)!≡(-1) (mod P)