Experimental Physics III Experimental Foundations of Quantum Physics

Transkript

1 Experimental Physics III Experimental Foundations of Quantum Physics Frank Cichos Lecture 1

2 Lectures and Seminars Lectures Prof. Dr. Frank Cichos Monday: 11:00-12:30 Uhr GrHS Thursday: 11:00-12:30 Uhr GrHS Seminars Martin Fränzl, Tobias Thalheim Tuesday: 07:30-09:00 SR 532 Friday: 13:30-15:00 SR 532 Room 322 Experiments Uwe Weber

3 Vorlesung Why? Understanding of experimental and theoretical approaches to problems of physics Important Information The exercises will start in the week of October 16, The first exercise sheet will be be available on October 9, 2017 on this website. The solutions to the exercise sheets have to be handed in Mondays before the lecture. For every solved problem 1 point can be obtained. Prerequisite for the admission to the examination are 50 % of the total points. Books for the Lectures Demtröder: Atoms, Molecules and Photons, Springer 2010 (amazon) Tipler, Mosca: Physics for Scientists and Engineers, Freeman 2008 (amazon) Haken, Wolf: The Physics of Atoms and Quanta: Introduction to Experiments and Theory, Springer 2005 (amazon) Alonso, Finn: Physics, Addison Wesley 1996 (amazon) Additional Material Visualizations of quantum mechanics (1D, 2D, 3D) Visualizations of the hydrogen atom Weak measurements: The following articles provide theoretical insights into quantum mechanical measurements, but use the bra ket formalism, which is not discussed in the lecture: Jakobs und Steck, Brun and Tamir und Cohen

4 Jupyter Notebooks

5 Jupyter Notebooks

6 Jupyter Notebooks

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11 Contents 1. Introduction/Atoms/Structure of Matter 1.1. Concept of the Atom Atoms Mass of an Atoms Size of an Atom Ingredients of Atoms, Atom models, Scattering 1.2.Electromagnetic Radiation as Particle Black Body Radiation, Planck s Radiation Law Photoeffect Compton Effect Photon Gas Spektrum Rydberg R H 2 2 n' n 1.3.Wave Character of Particles Matter Waves Wave-Particle-Duality Uncertainty Relation Bohr s Atom Model Emission/Absorption Lines Atom Hohlraumstrahlung Lichtquanten Planck Rutherford d d E 4 sin e h h k T B 0 1 h Einstein 2 Sommerfeld Bohr debroglie h mv x p h Heisenberg E H Schrödinger

12 Contents 2. Introduction to Quantum Mechanics 2.1.Wave function Indistinguishability Measurement Process Quantum Interference 2.2.Schrödinger-Equation 2.3.Applications of SE Free Particle Potential Step Tunnel Effect Box Potential Harmonic Oscillator Problems with spherical Symmetry 2.4.Operators Expectation Value Eigenvalue Commutation

13 Contents 3. The Hydrogen Atom 3.1.Wave function of the H-Atoms 3.2.H-Atom in Magnetic Fields Zeeman-Effect Electron Spin Fine Structure Anomalous Zeeman-Effect 3.3.Hyperfine Structur 3.4.Lamb-Shift Vacuum Fluctuations Casimir Effect

14 Contents 4. Atoms with Multiple Electrons 4.1.Pauli-Prinziple Fermions and Bosons Symmetry of the Wave Function 4.2.Helium Atom 4.3.Coupling of Angular Momenta LS-Coupling jj-coupling 4.4. Occupation Rules Hund s Rules Periodic System

15 Contents 5. Coupling of Atoms to em-radiation 5.1.Einstein Coefficients, Matrix Elements 5.2.Electric Dipole Radiation 5.3.Selection Rules Magnetic Quantum Number Orbital Angular Momentum Spin Total Angular Momentum 5.4.Line Width Lifetime Broadening Doppler Broadening homogeneous and inhomogeneous Broadening 5.5.X-Rays 5.6.Lasers

16 Contents 6. Molecular Physics 6.1.Hydrogen Molecule 6.2.Molecular Orbitals 6.3.Rotational and Vibrational Spectroscopy 6.4.Franck-Condon Principle

17 The Concept of the Atom Spektrum Rydberg R H 2 2 n' n Atom Hohlraumstrahlung Lichtquanten Planck Rutherford d d E 4 sin e h h k T B 0 1 h Einstein 2 Sommerfeld Bohr debroglie h mv x p h Heisenberg E H Schrödinger

18 Daltons Law - Mass Dalton (1803) All chemical elements consist of very small particles (atoms), which can not be further divided by chemical techniques. All atoms of the same chemical element have equal size, mass and quality, but they differ from the atoms of other elements. This means that the properties of a chemical element are determined by those of its atoms. When a chemical element A reacts with an element B to form a compound AB n (n = 1, 2,...) each atom of A recombines with one or several atoms of B and therefore the number ratio N B /N A is always a small integer. 2 H + O H O m H + m H 2 1AME + m O 16 AME 18 AME 2

19 Gay-Lussac Law - Volumes Gay-Lussac When two or more different gases completely recombine to form a gaseous chemical compound, the ratio of the volumes of reactands and reaction products at equal pressure and temperature is always given by the ratio of small integer numbers. Avogadro Amoleculeisthesmallestparticleofasubstance that determines the properties of this substance. It is composed of two or more atoms. At equal pressures and temperatures, the same volume of different gases always contains the same number of molecules.

20 Avogadro Constant N A = 6, (10) mol 1 1mol is the quantity of a substance that contains the same number of particles (atoms or molecules) as kg of carbon 12 C. V M = 22,413996(37) dm 3

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22 Brownian Motion A. Brongniard R. Brown L. Boltzmann A. Einstein L. Boltzmann

23 Field Emission Microscope a) + Heizung leitende Schicht R Wolfram- Spitze Feldlinien Bariumvorrat ZnS- Schirm b) vergrößertes Bild der Spitze r r ~ > 10 nm

24 Scanning Tunneling Microscope - STM x y x x-piezo Spitze z y y Regelverstärker Tunnelstrom y Monitor z x Abb Arsen-Atome an der Oberfläche eines Galliumarsenid-Einkristalls, sichtbar gemacht mit einem Rastertunnelmikroskop (Bildgröße 17 nm 17 nm). Nichtperiodische Strukturen wie Leerstellen und Stufen können auf atomarer Skala untersucht werden. Mit freundlicher Genehmigung von A.J. Heinrich, M. Wenderoth und R.G. Ulbrich, Göttingen

25 How heavy are atoms? How large are atoms? Are atoms indivisible?

26 Atomic Mass

27 Electrolysis - + from electrolysis Faraday s law: N A = F=NA e= C/mol current time elementary charge atomic mass deposited mass + - AgNO3 Ag + + NO3 - needs the elementary charge(e.g. Millikan)

28 Millikan Experiment Determination of the elementary charge

29 Atomic Size

30 van der Waals Gas p + a V 2 M (V M b)=rt V a = b 4N A

31 X-Ray Diffraction B) Röntgenbeugung " " d Notwendig für konstruktive Interferenz: constructive interference 2s = m s Laue-diffraction - on single crystals, polychromatic light - points sin( ) = s d 2d sin( ) = m Bragg-diffraction - monochromatic light, angular variation Debye-Scherrer diffraction - polycrystalline material, monochromatic light - cones

32 Laue Diffraction - Silicon Crystal

33 X-Ray Spectrum Fig. 4: X-ray intensity of copper as a function of the glancing angle LiF (100)-monocrystal as Bragg analyser Anode voltage U = 25 kv. Fig. 2: Energy levels of copper (z = 29).

34 Bremsstrahlung Spectrum

35 Crystal Structure Netzebenenabstand: d = 0,201 nm Gitterkonstante: a = nm

36 Crystal Structure

37 Debye Scherrer Diffraction 1 3 MgO diagram from the book Gerthsen, Physics