Lecture 3 Review of Quantum Physics & Basic AMO Physics
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1 Lecture 3 Review of Quantum Physics & Basic AMO Physics How to do quantum mechanics QO tries to understand it (partly) Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 1
2 Every Student Should Know How to signup to receive emergency text messages: Purdue Emergency Preparation Resources: An in case of emergency section/info has been added to syllabus Shots Fired on Campus: When Lightning Strikes --- a training video on how to respond to shooting In-door sheltering place inside physics building for none-fire related emergency More details, see syllabus & physics building emergency plan Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 2
3 This Lecture Review key concepts from quantum mechanics & AMO (cf. *FQ Chap3; also of interests: *FS Appendix; *Ken Krane Modern Physics *D. Griffiths: intro quantum mechanics * (AMO): Chris Foot, atomic physics Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 3
4 Some most important model systems in QM 2-state QM (d=2, simplest hilbert space) spin-1/2 ( & ) photon 2-polarization ( & ) Particle in box /1D Schrodinger Harmonic oscillator Hydrogen atom AMO physics Periodic potential solid state physics Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 4
5 Foundations of QM: early milestones Photon (Planck blackbody radiation) E=hf Photo-electric effect & Compton scattering (light matter interaction) PE can measure Planck constant Spectroscopy (atomic physics/astronomy) --- start from hydrogen --- Bohr s model (atom/matter quantized levels) Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 5
6 Birth of photon: birth of quantum Black body radiation Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 6
7 Photoelectric Effect Experimental Setup Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 7
8 Experimental Results Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 8
9 Einstein s Theory Conservation of energy yields: where is the work function of the metal. Explicitly the energy is The retarding potentials measured in the photoelectric effect are the opposing potentials needed to stop the most energetic electrons. Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 9
10 Quantum Interpretation The kinetic energy of the electron does not depend on the light intensity at all, but only on the light frequency and the work function of the material. Einstein in 1905 predicted that the stopping potential was linearly proportional to the light frequency, with a slope h, the same constant found by Planck. From this, Einstein concluded that light is a particle with energy: Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 10
11 Spectrum of Ball Lightning Hydrogen Spectrum Observation of the Optical and Spectral Characteristics of Ball Lightning Jianyong Cen, Ping Yuan, and Simin Xue Phys. Rev. Lett. 112, (2014) Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 11
12 Conceptual/theory Matter wave; wave-particle duality (De Broglie) Energy, momentum, wavelength, for free particle [dispersion] Uncertainty principle (Heisenberg) Fourier transform picture Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 12
13 Wave optics: diffraction (circular) Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 13
14 Energy-momentum-wavelength Wave-particle duality Massless particle (photon) Massive particle (eg. electron) Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 14
15 Theory/Formulation Schordinger equation/wavefuction Matrix formulation (Heisenberg) Dirac bra-ket quantum state/hilbert space QED and QFT Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 15
16 Schrodinger Eq. (time dependent) Hamiltonian Example: free particle Eigen states & eigen values => stationary state Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 16
17 Should know Example: free particle Probability density Normalizable (bound) vs unnormalizable (extended) state Superposition state Measurement (!.. weak measure) & expectation value/variance Commutator/commutation & general uncertainty principle E-t uncertainty Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 17
18 Theory/Formulation Schordinger equation/wavefuction Matrix formulation (Heisenberg) Dirac bra-ket quantum state/hilbert space Hamiltonian [ Abrahams example ] QED and QFT Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 18
19 Theory/Formulation Schordinger equation/wavefuction Matrix formulation (Heisenberg) Dirac bra-ket quantum state/hilbert space Wave function <-> vector in Hilbert space QED and QFT: Feynman diagram Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 19
20 Particle in a box/1d Schrodinger Infinite square well (uncertainty) Finite square well 1D scattering state (refection & transmission --- quantum reflection & tunneling, even resonant tunneling ) Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 20
21 Harmonic oscillator Harmonic trap Quantized EM fields Harmonic length Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 21
22 Energy-momentum-wavelength Wave-particle duality Massless particle (photon) Massive particle (eg. electron) Phase vs group velocity Dirac vs Schrodinger eq. (E H) Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 22
23 AMO (Atomic and Molecular & Optical Physics) Some Key Concepts Not really Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 23
24 Hydrogen Atom (Z=1) Bohr model Schrodinger equation Hydrogenic atom /ion Dopant in semiconductor.. Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 24
25 (quantum) Angular Momentum Orbital Spin (intrinsic angular momentum) Angular momentum addition, S-O coupling Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 25
26 Hydrogen atom wavefunction (for the electron orbit) Ψ (, r θφ, ) = R () r Θ () θφ () φ = R () r Y (, θφ) nlm,, nl, lm, m nl, lm, Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 26
27 Nomenclature 1/21/ Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 27
28 Probability Functions for a few states of H 1/21/ Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 28
29 Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 29
30 Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 30
31 n=1,l=0 Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 31
32 Finer structures Fine structure Hyperfine structure 21cm Zeeman effect (B field) Stark effect (E field) Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 32
33 Periodic Table of Elements each column have similar properties Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 33
34 Order of filling atomic orbitals Why filling the orbitals: Pauli exclusion principle 4s before 3d M (n=3) shell [draw levels on board L (n=2) shell K (n=1) shell subshell by l (s, p, d, f), each can accommodate 2(2l+1) elec Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 34
35 for n>=3. s & p orbitals more penetrating (can get closer to nucleus) ---- lower in energy d, f orbitals less penetrating (cannot get as close to nucleus) ---- higher in energy consequence in filling order, (4s, 3d, 4p), (5s, 4d, 5p), (6s, 4f/5d, 6p) etc. [with few exceptions] 3s 3p 3d ---- turns out 4s will come lower! Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 35
36 Periodic Table of Elements Alkaline earth each column have similar properties inert gas halogen Transition metal (elements) alkali f f (rare earth) Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 36
37 A few concepts Outer electrons (most important for usual chemical/physical properties, & optical transition), screening of nucleus charge by inner electrons (Z eff ) [example excited state approach hydrogenic atom] Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 37
38 not periodic behavior! Inner electron ( core electron) --- much more tightly bound, X-ray absorption edge and X-ray transition [K, L x-rays, etc.], Morseley s law to determine atomic Z # (K absorption edge) (K α ) Purdue University Spring 2016 Prof. Yong P. Chen (yongchen@purdue.edu) Lecture 3 (1/19/2016) Slide 38
39 Molecules How do molecules form (bonding) Molecular spectra Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 39
40 Molecular bonding Atomic orbitals interact and form molecular orbitals Bonding and anti-bonding orbitals Covalent bond H2+, H2 molecule, s-s bond P-p bond, eg. N2, O2 S-p bond, HCl, etc. Sp hybrid, involving C, Si etc. Ionic bond Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 40
41 rotation Vibration and Rotation quantum states 2B(J+1) BJ(J+1) vibration hf Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 41
42 Molecular potentials, ro-vibration levels & spectra hf HCl 2B Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 42
43 Some Modern Areas in AMO Physics Atomic/molecular structure and spectroscopy Few-body physics, chemical physics Precision measurements, fundamental constants, beyond standard model physics, atomic clocks Ultracold atoms/molecules, quantum gases ---BEC, fermi gas etc. Ultrafast science (from fs to as), quantum dynamics quantum physics & technology: quantum information/computing/communication, quantum control, quantum optics Laser physics: ultra-intense/fast lasers, light-matter interaction etc. Purdue University Spring 2016 Prof. Yong P. Chen Lecture 3 (1/19/2016) Slide 43
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