《无机化学 Chemical Theory》课程教学资源（讲稿）Part I Basic concepts of Quantum mechanics Chapter 1 The Basic Concepts of Quantum Mechanics

IntroductiontoQuantumMechanics主讲：苏培峰supi@xmu.edu.cn曾呈奎楼B409助教：An half semester course on non-relativistic quantum mechanics which is primarily intendedforundergraduatechemistrymajors

Introduction to Quantum Mechanics An half semester course on non-relativistic quantum mechanics which is primarily intended for undergraduate chemistry majors. 1 助教： 曾呈奎楼B409 主讲：苏培峰 supi@xmu.edu.cn

1.The basic concepts of quantum mechanics2. Simple cases3.Operators4.Angular Momentum5. The hydrogen atom6.Many-electron atoms7.Approximate methods -the Variation Method8.Diatomic molecules

1. The basic concepts of quantum mechanics 2. Simple cases 3. Operators 4. Angular Momentum 5. The hydrogen atom 6. Many-electron atoms 7. Approximate methods - the Variation Method 8. Diatomic molecules 2

MathematicsYou will find almostall the mathematics used inthis course surprisinglyfamiliar. Thebulk of it is differentiation and integration of standard expressions (such as x2, sin xexp(-x), and so on), plus the usual algebraic manipulation and

You will find almost all the mathematics used in this course surprisingly familiar. The bulk of it is differentiation and integration of standard expressions (such as x 2 , sin x, exp(-x 2 ), and so on), plus the usual algebraic manipulation and . Mathematics 3

Quantum Mechanics 1: Foundations, N. J. B. Green. OxfordChemistryPrimers,No.48Introduction to Quantum Mechanics, D.J.Griffiths, 2nd Edition,(PearsonPrenticeHall,UpperSaddleRiverN,2005)Molecular Quantum Mechanics, P. W. Atkins and R. S. Friedman,OxfordUniversityPress

Quantum Mechanics 1: Foundations, N. J. B. Green. Oxford Chemistry Primers, No. 48 Introduction to Quantum Mechanics, D.J. Griffiths, 2nd Edition, (Pearson Prentice Hall, Upper Saddle River NJ, 2005). Molecular Quantum Mechanics, P. W. Atkins and R. S. Friedman, Oxford University Press 4

Chapter 1.The basic concepts of guantum mechanics1.Black-BodyRadiationPlanck's constant:h = 6.626 × 10-34 J-sE=nhv2.ThephotoelectriceffectAcorpusculartheoryoflight (photons)8=hvh=Planck'sconstantp= h/α3. Bohr model

Chapter 1. The basic concepts of quantum mechanics 1. Black-Body Radiation 2. The photoelectric effect A corpuscular theory of light (photons)  = h h = Planck’s constant p = h/ 3. Bohr model E = nh Planck’s constant: h = 6.626  10-34 Js 5

ExperimentsParticles Behaving as Waves:Waves Behaving as ParticlesSinglephoton/electron double slit experimentThephotoelectric effect1801, Young1905,Einstein1920s, TaylorComptonEffect1974,Merli,Missiroli,Pozz1923, ComptonElectron Diffraction:1925,Davisson and GermerIntroductionandorientationMolecularQuantumMechanics0.1Black-body radiation120.2Heatcapacities0.33The photoelectric andComptoneffects40.4Atomicspectra

Experiments 1801, Young 1920s, Taylor 1974, Merli, Missiroli, Pozz Particles Behaving as Waves: Single photon/electron double slit experiment Electron Diffraction: 1925, Davisson and Germer Waves Behaving as Particles The photoelectric effect 1905, Einstein Compton Effect 1923, Compton Molecular Quantum Mechanics 6

1.1Thewave-particleduality of microscopicparticlesDe BroglieDe Broglie consideredthatthe wave-particlerelationshipinlightis alsoapplicabletoparticlesofmatter,i.eh=Planck'sconstant,E=-hvp = particle momentum,p=h/Λ入=deBrogliewavelength1929Thewavelengthofaparticlecouldbe determined by=h/p=h/mvIntroduction andorlentation10.1Black-bodyradiation20.2Heat capacities30.3ThephotoelectricandComptoneffects40.4Atomicspectra50.5Theduality ofmatter

1.1 The wave-particle duality of microscopic particles De Broglie 1929 De Broglie considered that the wave-particle relationship in light is also applicable to particles of matter, i.e. E=h p=h/ h = Planck’s constant, p = particle momentum,  = de Broglie wavelength The wavelength of a particle could be determined by = h/p = h/mv 7

ThedeBroglieWavelengthsof SeveralparticlesParticlesMass (g)入(m)Speed (m/s)9 × 10-281.07 × 10-4Slowelectron9×10-281 × 10-105.9 × 106Fastelectron6.6 × 10-247 × 10-151.5 ×107Alphaparticle7 × 10-291.00.01One-gram mass2 × 10 -3414225.0Baseball4 × 10 -636.0 × 10273.0×104Earth

The de Broglie Wavelengths of Several particles Particles Mass (g) Speed (m/s)  (m) Slow electron 9  10 - 28 1.0 7  10 -4 Fast electron 9  10 - 28 5.9  106 1  10 -10 Alpha particle 6.6  10 - 24 1.5  107 7  10 -15 One-gram mass 1.0 0.01 7  10 - 29 Baseball 142 25.0 2  10 - 34 Earth 6.0  1027 3.0  104 4  10 - 63 8

The wave-particle duality. Wave (i.e., light)- can be wave-like (diffraction)-canbeparticle-like(p-h/2).Particles- can be wave-like (2 =h/p)- can be particle-like (classical)Wave-particle duality is the concept that every particle may be partly described in termsnot only of particles, but also of waves. It expresses the inability of the classical concepts'particle"or"wave"tofully describethe behaviour of quantum-scale objects.Becauseparticles sometimes behave like waves or exhibit waveproperties, its hard to measurelocationsandvelocitieswithprecision

The wave-particle duality • Wave (i.e., light) - can be wave-like (diffraction) - can be particle-like (p=h/) • Particles - can be wave-like ( =h/p) - can be particle-like (classical) Wave–particle duality is the concept that every particle may be partly described in terms not only of particles, but also of waves. It expresses the inability of the classical concepts "particle" or "wave" to fully describe the behaviour of quantum-scale objects. Because particles sometimes behave like waves or exhibit wave properties, its hard to measure locations and velocities with precision. 9

TheUncertaintyPrincipleHeisenberg'sinsightBohr,Heisenberg,Pauli(LtoR)hAxApz4元The more precisely the position is determined, the lesspreciselythemomentumisknowninthisinstant,andvice versa.--Heisenberg, uncertainty paper,1927·Classical: the error in the measurement depends on the precision of the apparatus, could bearbitrarily small..Quantum: it is physically impossible to measure simultaneously the exact position and theexactvelocityofaparticleThe description of the behavior of electrons in atoms requires a completely new quantumtheory

•Classical: the error in the measurement depends on the precision of the apparatus, could be arbitrarily small. •Quantum: it is physically impossible to measure simultaneously the exact position and the exact velocity of a particle. The description of the behavior of electrons in atoms requires a completely new “quantum theory”. The Uncertainty Principle 4 h x p     10