范康年物理化学英文版chapter1

1、2022/9/25Chemistry Department of Fudan University1Physical Chemistry2022/9/25Chemistry Department of Fudan University2Chapter One Introduction to Quantum Mechanics 1020 meters 10-20meters 1010years 10-18seconds 1013stars 10 atomsCan we describe the universe using an uniform theory, especially at the

2、 atomic level?The WORLD2022/9/25Chemistry Department of Fudan University3Classical (Newtonian) MechanicsMaxwells Theory of Electricity and MagnetismIn the late of nineteenth century, some physicists believed that the theoretical structure of physics was complete, is it true?1-1 Naissance of the Quan

3、tum Mechanics2022/9/25Chemistry Department of Fudan University41900190519111913Max Planck explains blackbody radiation in the context of quantized energy emission: Quantum theory is born.Albert Einstein proposes that light, which has wavelike properties, also consists of discrete, quantized bundles

4、of energy, which are later called photons.Ernest Rutherford proposes the nuclear model of the atom.Niels Bohr proposes his planetary model of the atom, along with the concept of stationary energy states, and accounts for the spectrum of hydrogen.2022/9/25Chemistry Department of Fudan University5Arth

5、ur Compton observes that x-rays behave like miniature billiard balls in their interactions with electrons, thereby providing further evidence for the particle nature of light.Louis de Broglie generalizes wave-particle duality by suggesting that particles of matter are also wavelike.Wolfgang Pauli en

6、unciates the exclusion principle.Werner Heisenberg, Max Born, and Pascual Jordan develop matrix mechanics, the first version of quantum mechanics, and make an initial step toward quantum field theory.19231923192519252022/9/25Chemistry Department of Fudan University6192619271928Erwin Schrodinger deve

7、lops a second description of quantum physics, called wave mechanics. It includes what becomes one of the most famous formulae of science, which is later known as the Schrodinger equation.Heisenberg states his Uncertainty Principle, that it is impossible to exactly measure the position and momentum o

8、f a particle at the same time.Dirac presents a relativistic theory of the electron that includes the prediction of antimatter.2022/9/25Chemistry Department of Fudan University7A picture of some famous physicists in 1927A.EinsteinCurieM.PlanckLorenzoLangevinDebyeBraggDiracPauliHeisenbergBoreDe Brogli

9、eComptonBornThese four works contributed substantially to the foundation of modern physics and changed views on space, time, and matter. 2022/9/25Chemistry Department of Fudan University9Quantum Mechanics is one of the most profound and beautiful creations of the human mind. Their beauty is transcen

10、ded only by those things that are beyond the reach of man, such as the smile of a child.2022/9/25Chemistry Department of Fudan University10任何物体都能发光，发热 ( 观察加热铁的变化）如何定量描述物体之间的热量传递？热辐射场 靠电磁波传热热平衡条件：放热=吸热（能量）基尔霍夫定律： 辐射本领/吸收本领=常量=辐射照度（单位面积）均匀场寻找物体，吸收本领=1，可通过测量辐射本领，来得到辐射照度（辐射场的特征）2022/9/25Chemistry Depart

11、ment of Fudan University11Blackbody is a substance that can absorb all frequencies of radiation falling on it but do not reflect radiation.Radiation energy density mT(u） (J/(m3 Hz)2022/9/25Chemistry Department of Fudan University122022/9/25Chemistry Department of Fudan University131. The radiating a

12、toms or molecules of the blackbody can emit and absorb electromagnetic energy as coming in small packets. The packets of energy are called quanta and are only in multiples of the minimum energy . 2. The minimum energy . M.Planck2022/9/25Chemistry Department of Fudan University14A mode for an electro

13、magnetic wave in a cavity must satisfy the condition of zero electric field at the wall. If the mode is of shorter wavelength, there are more ways you can fit it into the cavity to meet that condition. Careful analysis by Rayleigh and Jeans showed that the number of modes was proportional to the fre

14、quency squared.2022/9/25Chemistry Department of Fudan University15Lower FrequencyPlancks EquationRauleigh-Jeans EquationHigher Frequencyenergy density2022/9/25Chemistry Department of Fudan University16Problem:a) Use the fact that to show that the radiation energy emitted per second by unit area of a

15、 blackbody is . b) The suns diameter is m and its effective surface temperature is 5800 K. Assume the sun is a blackbody and estimate the rate of energy loss by radiation from the sun.c) Use to calculate the relativistic mass of the photons lose by radiation from the sun in a year.(Note: c/4 )2022/9

16、/25Chemistry Department of Fudan University172022/9/25Chemistry Department of Fudan University18金属Photoelectric Effect2022/9/25Chemistry Department of Fudan University19. It is the frequency of the light, not the intensity, determines whether or not electrons are emitted. The frequency that is just

17、sufficient to excite the electron, is known as the threshold frequencyP.Lenard (1905 Nobel Prize）2022/9/25Chemistry Department of Fudan University20Classical Physics：The energy of a wave depends only on its intensity. Whether or not electrons are emitted should depend on the energy of the radiation.

18、 Light even with low intensity, regardless of its frequency, should be able to excite electrons if long enough time is allowed for the absorption. 2. The number of electrons emitted is proportional to the intensity, and the electron emission occurs as soon as the radiation reaches the metal surface.

19、2022/9/25Chemistry Department of Fudan University212. Photons obey the laws of conservation of energy and momentum when the photons interact with the material. Einsteins Theory on Photon1. Light itself is a beam of particles, each of which has energy equal to and momentum to .3. The intensity of lig

20、ht is proportional to the number of photons per unit volume in the beam.2022/9/25Chemistry Department of Fudan University22Origin of the Photoelectric effect kinetic energy K = E (radiation)- work function W2022/9/25Chemistry Department of Fudan University23Comptons effect, Nobel Prize in 1927invest

21、igated the scattering of monochromatic x-ray and found that the scattered beam consists of radiation of two different wavelengths, one as the same as the original beam and the other slightly longer.2022/9/25Chemistry Department of Fudan University24Problem:The work function of K is 2.2eV and that of

22、 Ni is 5.0eV.a) Calculate the threshold frequencies and wavelengths for these two metals.b) Will violet light of wavelength 4000 cause the photoelectric effect in K? In Ni?c) Calculate the maximum kinetic energy of the electron emitted in b).2022/9/25Chemistry Department of Fudan University25Bohrs A

23、tomic TheoryWhat is the rule governing the atomic spectra2022/9/25Chemistry Department of Fudan University26J.J.Balmers seriesJ.R.Rydbergs seriesHow to explain these rules？-The Model of Atomic StructureSome empirical relationships:2022/9/25Chemistry Department of Fudan University27J.J.TomsonJ.J.Thom

24、sons Modelpudding model2022/9/25Chemistry Department of Fudan University28E.Rutherfords model1.The nucleus of an atom is much smaller than the atom itself;2. The electrons revolve around the densely positively charged nucleus;3. The size of atom is determined by the size of the electronic orbitals20

25、22/9/25Chemistry Department of Fudan University29Rutherfords model presented a serious problem in terms of classical physics. 1. An orbiting charged particle must continuously lose energy. The electron would therefore fall into the nucleus, and the atom would not survive.2.The kinds of atom are limi

26、ted, why?Bohrs atomic theory= Plancks Theory + Einsteins theory of radiation + Rutherfords concept of atom2022/9/25Chemistry Department of Fudan University30is a positive integer1. There are certain allowed energy, known as stationary states in the atom.2. These states are characterized by discrete

27、values on the angular momentum3. When an electronic transition occurs between two states of energies, the frequency is given by2022/9/25Chemistry Department of Fudan University31Application to hydrogen atomBohr radius109737.31cm-12022/9/25Chemistry Department of Fudan University32Bohr & Copenhagen S

28、choolCorrection of Bohrs Theory109677.60cm-1109737.31cm-1Sommerfeld2022/9/25Chemistry Department of Fudan University33Problem:On the basis of the Bohr theory, calculate the ionization energy of the hydrogen atom and the linear velocity of an electron in the ground state of the hydrogen atom.2022/9/2

29、5Chemistry Department of Fudan University34Dual Theory of RadiationNewtonHuygensYoungFresnel2022/9/25Chemistry Department of Fudan University35A.Einsteins RelationshipInteraction PropagationWave-particle dualityNewtonMaxwellEinstein2022/9/25Chemistry Department of Fudan University36Elementary partic

30、les such as electrons can also have wave properties, just as radiation has particle properties. de BroglieINTEGER? de Broglies relationDual Theory of ParticleLouis de Broglie generalizes wave-particle duality by suggesting that particles of matter are also wavelike2022/9/25Chemistry Department of Fu

31、dan University37 Show the de Broglie wavelengths of a 10 g bullet moving at 10 m/s and a electron (9.110-31 kg) moving at 108 cm/s.The extremely small size of wavelength indicates that quantum effects are unobservable for the motion of macroscopic objects. 2022/9/25Chemistry Department of Fudan Univ

32、ersity38De Broglies prediction was confirmed experimentally in 1927C.J.Davtsson & L.H.GermerLow Energy Electron Diffraction ( LEED )2022/9/25Chemistry Department of Fudan University39LEED in model catalysis2022/9/25Chemistry Department of Fudan University40G.P.Thomson 2022/9/25Chemistry Department o

33、f Fudan University41The scattering of electron from a golden crystal.The scattering of electron from a nickel golden crystal.The Rule of Silver Coin2022/9/25Chemistry Department of Fudan University42ParticleWave2022/9/25Chemistry Department of Fudan University43Quantum mechanicssays a lot, but does

34、not really bring us any closer to the secret of the Old One. I, at any rate, am convinced that He does not throw dice. - A. Einstein2022/9/25Chemistry Department of Fudan University44There was a time when the newspapers said that onlytwelve men understood the theory of relativity. I do notbelieve th

35、ere ever was such a time. There might havebeen a time when only one man did , because he was theonly guy who caught on , before he wrote his paper. Butafter people read the paper a lot of people understood thetheory of relativity in some way or other , certainly morethan twelve. On the other hand ,

36、I think I can safely saythat nobody understands quantum mechanics. 著名理论物理学家、诺贝尔奖获得者 费曼2022/9/25Chemistry Department of Fudan University45The Uncertainty PrincipleProblem：Can we make accurate measurements of both two properties, such as the momentum and position, at same time?It is impossible, becaus

37、e any technique for measuring one of them will necessarily disturb the system and will cause the measurement of the other one to be imprecise.2022/9/25Chemistry Department of Fudan University46 Problem:The electron does not fall into the nucleus, why?2022/9/25Chemistry Department of Fudan University

38、47A.H.Zewail & FemtochemistryNobel Prize in 1999Application of Uncertainty Principle - lifetime of excited state2022/9/25Chemistry Department of Fudan University48Problem:What is the de Broglie wavelength of an oxygen molecule at room temperature? Compare this to the average distance between oxygen

39、molecules in a gas at 1 bar at room temperature.What is the de Broglie wavelength of an electron that has been accelerated through a potential difference of 100V.What is the width in energy domain of a 4fs pulse?2022/9/25Chemistry Department of Fudan University49Matrix MechanicsW.HeisenbergWave Mech

40、anicsE.SchrodingerDiracHow do we describe the behavior of micro-particles ?2022/9/25Chemistry Department of Fudan University50Wavefunction: Matter is described by a wave, called the wavefunction , that depends upon the coordinates and time. In general, well-behaved wavefunction must be finite, singl

41、e-valued, and continuous at all points.Stationary state wavefunction& Time-dependent wavefunction gives the probability density for finding the particle at a given location q in space.Quadratically integrable2022/9/25Chemistry Department of Fudan University51Borns Interpretation 对应于空间的一个状态，就有一个伴随这状态

42、的德布罗依波的几率。若与电子对应的波函数在空间某点为零，这就意味着在这点发现电子的几率小到零。 M.BornThe intensity of a particle at some point is proportional to the probability density at that point. 2022/9/25Chemistry Department of Fudan University52the Scattering of Electrons2022/9/25Chemistry Department of Fudan University53Linear Combinatio

43、n of Wavefunction2022/9/25Chemistry Department of Fudan University54Coherent control of reaction2022/9/25Chemistry Department of Fudan University55Problem:1. A possible eigenfunction for the system is: Show that , the probability, is independent of time.2. Prove that m must be an integer in order fo

44、r the function to be an acceptable wave function.2022/9/25Chemistry Department of Fudan University56FunctionsFunction2022/9/25Chemistry Department of Fudan University57OperatorsAn operator is a mathematical operation that is applied to a function. 2022/9/25Chemistry Department of Fudan University58e

45、qualityadditionf(x) is an arbitrary function2022/9/25Chemistry Department of Fudan University59Multiplication & CommutationMultiplicationCommutationThe multiplication of operators is in general not commutative.2022/9/25Chemistry Department of Fudan University60Linear operatorHermitian operatorEigene

46、quationEigenfunctionEigenvalueDegenerate & DegeneracyDistributive Law2022/9/25Chemistry Department of Fudan University61Two important properties of Hermitian operatorTheorem 1: Their eigenvalues are real.Theorem 2: Eigenfunctions belonging to distinct eigenvalues are orthogonal2022/9/25Chemistry Dep

47、artment of Fudan University622022/9/25Chemistry Department of Fudan University632022/9/25Chemistry Department of Fudan University64Problem:Prove that momentum operator corresponding to is a Hermitian operator.2022/9/25Chemistry Department of Fudan University65Postulates of Quantum MechanicsThe first

48、 Postulate: A state of a quantum mechanical system is completely specified by a wavefunction that is a function of the coordinates of the particle and time.2022/9/25Chemistry Department of Fudan University66NormalizationOrthogonal2022/9/25Chemistry Department of Fudan University67The process of conv

49、erting a function for a classical system into the corresponding operator for the quantum mechanical system is formalized by the following rules:1) Each Cartesian coordinate in the Hamiltonian function is replaced by the coordinate itself.2) Each Cartesian component of linear momentum in the Hamilton

50、ian function is replaced by the operator of momentum. The second Postulate: Every classical observable is associated with a quantum mechanical operator.deducible from momentum representative2022/9/25Chemistry Department of Fudan University68Laplace OperatorObservables are represented by hermitian op

51、erators2022/9/25Chemistry Department of Fudan University69The third Postulate: The average (expectation) value of a physical observable associated with an operator is given by:where is the complex conjugate of . 2022/9/25Chemistry Department of Fudan University702022/9/25Chemistry Department of Fuda

52、n University71Schrdinger EquationTime-independent Schrdinger EquationTime-dependent Schrdinger Equationis called Hamiltonian2022/9/25Chemistry Department of Fudan University72A special case: Standing wave2022/9/25Chemistry Department of Fudan University73One-dimensional Box2022/9/25Chemistry Departm

53、ent of Fudan University742022/9/25Chemistry Department of Fudan University752022/9/25Chemistry Department of Fudan University761.They are alternately even and odd with respect to the center of the well2. As you go up in energy, each successive state has one more node3. They are mutually orthogonalPr

54、operties of Wavefunctions2022/9/25Chemistry Department of Fudan University77orthogonal2022/9/25Chemistry Department of Fudan University782022/9/25Chemistry Department of Fudan University79Two-dimensional Box2022/9/25Chemistry Department of Fudan University80Here they have positioned 48 iron atoms in

55、to a circular ring in order to corral some surface state electrons and force them into quantum states of the circular structure. The ripples in the ring of atoms are the density distribution of a particular set of quantum states of the corral. The artists were delighted to discover that they could p

56、redict what goes on in the corral by solving the classic eigenvalue problem in quantum mechanics - a particle in a hard-wall box. Quantum Corral2022/9/25Chemistry Department of Fudan University81Harmonic OscillatorSymmetricalstretchingAntisymmetrical stretchingScissoringRockingWaggingTwisting2022/9/

57、25Chemistry Department of Fudan University83Harmonic Oscillator2022/9/25Chemistry Department of Fudan University842022/9/25Chemistry Department of Fudan University88Zero-point EnergyUncertainty Principledefinite position / definite momentum2022/9/25Chemistry Department of Fudan University892022/9/25Chemistry Department of Fudan University90When a particle passes through a region that is classically prohibited, the process is called tunneling.2022/9/25Chemistry Department of Fudan University91Tunneling Effect of Stat