对原子径向距离期望值的进一步计算

由量子力学量平均值与算符的关系可知,对于连续归一的u(r)函数,有〈rλ〉=∞∫0rλu(r)2dr(1)当λ=-2时,引进变量ρ=ra0,对于E=En,u(r)函数满足d2unld2ρ 2Zρ-Z2n2-l(l 1)2runl=0(2)〈ρλ〉=a0∞∫0ρλu2nldρ(3)这里根据能级情况暂时假设l是连续变量,而n依赖于l的方式保持n-l是一整数,则径向本征函数unl对于l来说是连续可微的.由(2)式得到lun″lunl=l2Zn2-2Zρ l(l 1)2ρ=-2Z23n 2l 12ρ将此方程乘以u2nl,然后对ρ进行积分,得∫∞0u2nll(un″lunl)dρ=∫∞0unlun″lldρ-∫∞0un″lunlldρ=∞∫0unlun″lld…     

极坐标曲线周期的判定定理

在极坐标系中,由于点的极坐标的多值性,带来了一系列问题与在直角坐标系中讨论曲线有所不同。此文揭示了极坐标曲线ρ=f（θ）的周期与函数ρ=f（θ）的周期之间的数量关系,并给出了简捷而严格的证明,使求极坐标曲线的周期有了一个简便可行的方法。     

铁（Ⅲ）-邻菲罗啉间接光度法测定对乙酰氨基酚的含量

pH值为2～9的Fe(Ⅲ)溶液中,加入对乙酰氨基酚,将Fe(Ⅲ)定量还原为Fe(Ⅱ),Fe(Ⅱ)离子与邻菲罗啉形成橘红色配合物(λmax=511 nm).结果表明,对乙酰氨基酚含量(ρ)4.00～48.00μg·mL~(-1)范围内,配合物溶液吸光度与对乙酰氨基酚含量呈良好的线性关系,其线性回归方程为A=0.021ρ+0.052 8,线性相关系数r=0.999 7.方法用于感冒药中对乙酰氨基酚含量的测定,测定的相对标准偏差为0.3%～0.7%(n=10),加标回收率为95.6%～101.6%(n=10),方法检出限为0.71μg·mL~(-1),测定结果与药典法相近.     

块矩阵谱半径的估计

研究了块矩阵A=（Aij）与矩阵B=（bij）,bij={｜｜Aij-1｜｜-1,i=j,｜｜Aij｜｜,i≠j,的谱半径的关系,证明了ρ（A）≤ρ（B）,其中ρ（A）,ρ（B）分别是它们的谱半径.特别是,若A是块H-矩阵,则ρ（A）≤maxi{2｜｜Aii-1｜｜-1.}     

极坐标方程表示的曲线交点的求法

在极坐标系下,曲线C_i的方程记为 f_1(ρ,θ)=0(i=1,2). 一、交点坐标与方程组解的关系: 所谓方程j(ρ,θ)=0是曲线C的极坐标方程,即满足:①f(ρ,θ)=0的解对应的点都在曲线C上;②曲线C上任一点的极坐标(ρ,θ)都满足方程f(ρ,θ)=0.由于点的极     

ρ与ds/dθ的符号关系及应用

解力学问题时,自然坐标系是经常被采用的。教材中一般说ds/dθ等于曲率半径ρ。例题中则有时用ρ=ds/dθ,有时则用ρ=-ds/dθ,不说缘由,或说明甚简。部分人颇觉迷糊,却又找不到直接的答案。本文将首先论述各种情况下ρ与ds/dθ的符号关系,再以实例说明它在力学解题中的不同应用。为了简单起见,文中只讨论平面曲线。 一、ρ与ds/dθ的符号关系 ρ是曲线轨道上某点的曲率半径应为正值。设图1中曲线方程是     

关于ρ=±(x~2+y~2)~(1/2)中符号的确定

在曲线的极坐标方程化到曲线的直角坐标方程时,常用到ρ~2=x~2+y~2。故ρ=±(x~2+y~2)~(1/2)。怎样确定“+”、“-”号?现在举例说明如下: 1.用ρ=(x~2+y~2)~(1/2)的情况。例1.化极坐标方程e~ρ=2+cosθ为直角坐标方程。解.因为2+cosθ≥1,所以原方程中ρ≥0,因此ρ=(x~2+y~2)~(1/2)。由e~ρ=2+cosθ得ρe~ρ=2ρ+ρcosθ。从而原方程可化为 (x~2+y~2)~(1/2)e~((x~2+y~2)~(1/2))=2(x~2+y~2)~(1/2)+x。例2.把极坐标方程ρ=1+cosθ化为直角坐标方程。     

错在哪里

题:曲线C_1的方程是ρ=cosθ,曲线C_2的方程是ρ=1 cosθ,求曲线C_1与C_2交点个数.解 两曲线方程联立 ρ=cosθρ=1 cosθ得:cosθ=1 cosθ,即1=0,亦即θ无解,所以C_1与C_2的交点个数为0个.解答错了!错在哪里?错在忽视了极点的极角的任意性.     

极坐标系下曲线同一性的判定

[定理]设有曲线的极坐标方程:ρ=f(θ),(α<θ<β)…(1)与ρ=g(θ),(α-(2k+1)π<θ<β-(2k+1)θ)…(2)如果对于任意θ∈(α-(2k+1)π,β-(2k+1)π),恒有     

电介质中极化电荷密度的计算

给出了两种计算电介质中极化电荷密度的方法.(1)介质内部极化电荷密度等于极化强度矢量的散度的负值,ρP=-▽·P;(2)介质内部极化电荷密度与介质的极化率、介质内自由电荷密度以及极化率梯度与电场强度之间的相互作用有关,ρP=-χe/χe+1ρf-ε0/χe+1▽χe·E.针对电荷分布具有一定对称性的问题,分别利用这两种方法分析了电介质均匀且内部不存在自由电荷、电介质均匀但内部存在自由电荷以及电介质不均匀且内部不存在自由电荷情况下介质内部的极化电荷密度,并通过实例加以详尽的讨论.     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

风的曲线

Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose.     

团图为数的图中的闭团贯数

Given a graph G,a subgraph C is called a clique of G if C is a complete subgraph of G maximal under inclusion and |C|≥2. A clique-transversal set S of G is a set of vertices of G such that S meets all cliques of G. The clique-transversal number, denoted as TC (G), is the minimum cardinality of a clique-transversal set in G. The clique-graph of G, denoted as K (G), is the graph obtained by taking the cliques of G as vertices, and two vertices are adjacent if and only if the corresponding cliques in G have nonempty intersection. Let F be a class of graphs G such that F={G|K(G) is a tree}. In this paper the graphs in F having independent clique-transversal sets are shown and thus TC (G)/|G|≤1/2 for all G ∈ F.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.