-常州大学研究生试题

-常州大学研究生试题
-常州大学研究生试题

2009B 班量子力学考试试题——常州大学

姓名 韩小玉 得分

一、(30分)简答题

1.黑体辐射、光电效应和康普顿散射这三个实验说明了什么问题?

2.请阐述量子力学中的态叠加原理。

3.量子力学中表示力学量的算符是什么算符?有哪三个性质?

4.由所有的电子和光子组成的全同粒子体系分别是费米子还是玻色子?他们各有什么特点?

5.请说明什么是全同粒子?什么是全同性原理?以及描写全同粒子体系的波函数有什么性质?

二、(15分)证明题

1.[]x ?i L ?y ?z =,, 2. []y

x z L ?i L ?L ? =,, 3. []

0L ?p ?x x =, 三、(55分)计算题 1. (15分) 设粒子在一维势场

?????>∞≤≤<∞=a x a

x x x U ,,,0 00)(

中运动,求(1)粒子的能级和对应的波函数;(2)几率流密度。

2. (10分)已知粒子的波函数为0/N ),,(a r e r -=?θψ,求:

(1)归一化常数N ;(2)r 的平均值;

(3)势能r

e 2

-的平均值; (4)最可几半径. 3.(10分)设已知在Z L L ??2和的共同表象中,算符x

L ?的矩阵分别为 ????

? ??=010*******? x L 求它们的本征值和归一化的本征函数,最后将矩阵x L 对角化。

4.(10分)一体系在未受微扰作用时只有三条能级,在0H 表象中

????

? ??=)0(3)0(2)0(10000000?E E E H 现受到微扰????

? ??='c f e f b d e d a ?H

的作用,用微扰论分别求三个能级的二级近似能量。

5.(10分)求在自旋态)(21z S

χ中,

x S ?和y S ?的测不准关系:?)()(22=??y x S S

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大学英语测试题及答案

Test Three (A) I Reading Comprehension Passage One The man who, legend has it, escaped from an early grave when his uncle pulled him from drowning in a dirty pond is notorious for his dirty deeds but that what cannot be forgotten are his achievements in the 1986 World Cup. Forget the handball against England, feel the quality of his 50-yard solo goal in the same game and the near repeat performance in the semi-final against Belgium. The Argentina side of the 1986 was functional and hard-working but it was Maradona who fired them to the final and then set up two of the goals in their 3-2 win over West Germany in the final. In 1990, a barely-fit Maradona fought his way to the final where the Germans took their -match tears. In fact many rejoiced that such an ugly revenge. Few people shared Diego’s post brute of a team had lost. Eight years before, in Spain, Maradona , then newly arrived at Barcelona, disgraced himself by being sent off in a Second Phase game with Brazil. Even four years before that the 18-year-old Maradona was a source of great controversy when he was left out of the victorious squad that won on home ground. USA 1994 was the end for Maradona as a player. Right after the Nigeria game, he was picked for drugs-screening and tested positive for banned stimulant ephedrine (麻黄硷). He was banned from the rest of the tournament and the team fell apart, going out in the second round to Romania. 21. How many World Cups are mentioned in the passage? A) Three. B) Four.C) Five D) Six. 22.Which country won the 1990 World Cup? A)Argentina B) West Germany C) Romania D) England 23. Maradona won the World Cup. A) once B) twice C) three times D) four times 24.When in 1994, Maradona was driven out of the World Cup, he was close to . A) 18 B) 24 C) 26 D) 31 25. According to the passage, Maradona is a man . A) full of ideas B) with cruel behaviors C) having good luck D) of great controversy Passage Two Many companies have run into serious troubles trying to coordinate their sales and promotional efforts. For example, one firm authorized a large promotional drive to introduce a new product in Latin America. The promotion ran smoothly, but someone forgot to coordinate product delivery — ship the product. Consumers were confused and money was wasted when the promoted product was not available. To avoid such occurrences, all plans should be in writing and someone should be responsible for central coordination. Hence, risks are lessened and opportunities to save money may arise. Coca-cola, for instance, requires that all overseas marketing plans be submitted to the central office well in advance. This gives the company a chance to examine 1 / 6

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