授課教案1.ppt

1、量子力學Quantum mechanics,School of Physics and Information Technology Shaanxi Normal University,Requirements,(1) Class discipline,(2) Teaching log : Monitor,registry form: commissioner,Learn Think - Do What Why - How,Bilingual teaching/education (course) 雙語教學(課程),Some words,preface post face,Knowledge

2、知識,Language,teaching materials textbooks and references,obstruction,beyond the book,Quantum Mechanics,量子力學,Textbooks and references,Textbooks in Cinese,周世勛，曾謹言，喀慶林，等等,周世勛著，量子力學教程，高等教育出版社，1979年。 曾謹言編著，量子力學，科學出版社，1984年 曾謹言，量子力學（I,）,量子力學導論，2003. 錢伯初，量子力學基本原理和計算方法，甘肅人民出版社，1984.12. 倪光炯: 高等量子力學, 曾謹言、錢伯初，量

3、子力學專題分析（上,下），1990,1999 郭敦仁，數(shù)學物理方法，人民教育出版社，1965 梁昆淼，數(shù)學物理方法，人民教育出版社，,D. J. Griffiths，Introduction to Quantum Mechanics, Sara M. McMurry. Quantum mechanics. Paul Roman, Advanced Quantum Theory-An outline of the fundamental ideas, J. J. Sakurai，Modern quantum mechanics. R. Shankar. Principles of quantum

4、 mechanics. Feynman, The Feynman Lectures on Physics, Vol. 3; Quantum Mechanics Cohen-Tannoudji，Quantum Mechanics, Vol. 1 Quantum MechanicsNo.9: ter Haar, Problems in Quantum Mechanics,No.1: Quantum Mechanics, Vol. 1&2； Cohen-Tannoudji,No.2: The Principles of Quantum Mechanics；Dirac,No.3: Quantum Me

5、chanics；Landau,No.4: Problems and Solutions on Quantum Mechanics by Yung-Kuo Lim (Editor), Chung-Kuo KO Hsueh Chi Shu Ta Hsueh Physics Coaching Class,Introduction to Quantum Mechanics,David J.Griffiths,Your fortune,Good book,PREFACE PART THEORY 1 THE WAVE FUNCTION 1 1.1 The Schrdinger Equation 1 1.2

6、 The Statistical Interpretation 2 1.3 Probability 5 1.4 Normalization 12 1.5 Momentum 15 1.6 The Uncertainty Principle 18,CONTENT 目錄,2 TIME-INDEPENDENT SCHRDINGER EQUATION 24 2.1 Stationary States 24 2.2 The Infinite Square Well 30 2.3 The Harmonic Oscillator 40 2.4 The Free Particle 59 2.5 The Delt

7、a-Function Potential 68 2.6 The Finite Square Well 78,3 FORMALISM 93 3.1 Hilbert Space 93 3.2 Observables 96 3.3 Eigenfunctions of a Hermitian Operator 100 3.4 Generalized Statistical Interpretation 106 3.5 The Uncertainty Principle 110 3.6 Dirac Notation 118,4 QUANTUM MECHANICS IN THREE DIMENSIONS

8、131 4.1 Schrdinger Equation in Spherical Coordinates 131 4.2 The Hydrogen Atom 145 4.3 Angular Momentum 160 4.4 Spin 171 5 IDENTICAL PARTICLES 201 5.1 Two-Particle Systems 201 5.2 Atoms 210 5.3 Solids 218 5.4 Quantum Statistical Mechanics 230,PART APPLICATIONS 6 TIME-INDEPENDENT PERTURBATION THEORY

9、249 6.1 Nondegenerate Perturbation Theory 249 6.2 Degenerate Perturbation Theory 257 6.3 The Fine Structure of Hydrogen 266 6.4 The Zeeman Effect 277 6.5 Hyperfine Splitting 283 7 THE VARIATIONAL PRINCIPLE 293 7.1 Theory 293 7.2 The Ground State of Helium 299 7.3 The Hydrogen Molecule Ion 304,8 THE

10、WKB APPROXIMATION 315 8.1 The “Classical” Region 316 8.2 Tunneling 320 8.3 The Connection Formulas 325 9 TIME-DEPENDENT PERTURBATION THEORY 340 9.1 Two-Level Systems 341 9.2 Emission and Absorption of Radiation 348 9.3 Spontaneous Emission 355,10 THE ADIABATIC APPROXIMATION 368 10.1 The Adiabatic Th

11、eorem 368 10.2 Berrys Phase 376 11 SCATTERING 394 11.1 Introduction 394 11.2 Partial Wave Analysis 399 11.3 Phase Shifts 405 11.4 The Born Approximation 408 INDEX 420,PREFACE,Newtons mechanics,Maxwells electrodynamics,Einsteins relativity,Quantum mechanics,Not by one individual,1. Differences,Not be

12、 packaged,Still youth,舍赫拉查德,2. Characteristic of Quantum mechanics,No general consensus,Scheherazade,Can “do”, but cant tell what we are doing.,Implausible,Niels Bohr: “If you are not confused by quantum physics then you havent really understood it”.,Richard Feynman: ”I think I can safely say that n

13、obody understands quantum mechanics”.,3. Introduction of the textbook,This book is divided into two parts,Part I basic theory,Part II approximation method Applications,Chapter 1,Chapter 5,Chapter 6,Chapter 11,(5 Chapters),(6 Chapters,One-semester course,One-year course,(1) Structure,rudiments of lin

14、ear algebra,(2) Knowledge requirements for students,complex numbers,calculus and partial derivatives,Fourier analysis,Elementary classical mechanics,Maxwells electrodynamics,mathematical physics,Dirac delta function,Math,Physics,THE WAVE FUNCTION,PART THEORY,Chapter 1,1.1 The Schrdinger Equation 1 1

15、.2 The Statistical Interpretation 2 1.3 Probability 5 1.4 Normalization 12 1.5 Momentum 15 1.6 The Uncertainty Principle 18,(1) Classical mechanics:,Initial conditions:,1.1 The Schrdinger Equation,Classical mechanics,Quantum mechanics,(2) Quantum mechanics,Wave function,Schrdinger Equation,1.2 The S

16、tatistical Interpretation,What is the Wave function?,Borns statistical interpretation:,gives the probability of finding the particle at,point x, at time tor more precisely,Probability of finding the particle between a and b, at time t.,The shaded area represents the probability of finding the partic

17、le between a and b, at time t. The particle would be relatively likely to be found near A, and unlikely to be found near B.,The statistical interpretation introduces a kind of indeterminacy into quantum mechanics.,Quantum mechanics offers statistical information about the possible results.,Is it a f

18、act of nature, or a defect of theory?,Question? Where was the particle just before I made the measurement?,Do measure the position of the particle,Three plausible answers!,(1) The realist position: 現(xiàn)實主義立場,(2) The orthodox position: 正統(tǒng)的立場,(3) The agnostic position: 不可知論立場,The particle was at C.,The p

19、article wasnt really anywhere.,Refuse to answer.,Which is the right answer?,In 1964, John Bell,Showing that it will make an observable difference,The experiments show that the orthodox answer is right.,Immediate repetition of measurement,Zeno effect = remains on its initial state,Continuous evolutio

20、n = no measurement,discontinuous collapse = measurement,1.3 Probability,1.3.1 Discrete Variables,Age,Number,14,1,15,1,16,3,22,2,24,2,25,5,Number(age),The total number of people:,(1) The probability that the persons age would be j ?,(2) What is the most probable age ?,(3) What is the median age ?,(4)

21、 What is the average (or mean) age ?,the average value of age j is,(5) What is the average of the squares of the ages ?,Discussions:,The statistical quantities:,Average value,the most probable value,Median value,How to discriminate them ?,the number of elements,Deviation from the average,1.3.2 Conti

22、nuous Variables,age,16 years, 4 hours, 27 minutes,Continuous Value,interval : 16, 17 ,The probability in a sufficiently short interval is proportional to the length of the interval.,Infinitesimal intervals dx,Probability that an individual (chosen at random) lies between x and x+dx,The proportionality factor, , is called probability density.,The probability that x lies between a and b is given by the integral,1.4 Normalization,is the probability density for finding the particle at point,x, at time t.,A complex constant,We can choose complex constant A to meet above equa