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12 量子物理

12 量子物理. Sections. Photon and Matter Waves Compton Effect Light as a Probability Wave Electrons and Matter Waves Schrodinger ’ s Equation Waves on Strings and Matter Waves Trapping an Electron Three Electron Traps The Hydrogen Atom. 12-1 Photon and Matter Waves ( 光子和物質波 ).

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12 量子物理

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  1. 12 量子物理

  2. Sections • Photon and Matter Waves • Compton Effect • Light as a Probability Wave • Electrons and Matter Waves • Schrodinger’s Equation • Waves on Strings and Matter Waves • Trapping an Electron • Three Electron Traps • The Hydrogen Atom

  3. 12-1Photon and Matter Waves (光子和物質波) • Light Waves and Photons

  4. The Photoelectric Effect光電效應

  5. The experiment • First Experiment (adjusting V)– the stopping potential Vstop • Second Experiment (adjusting f)– the cutoff frequency f0 光電子的最大動能與光強度無關 低於截止頻率時即使光再強也不會有光電效應

  6. The plot of Vstopagainst f

  7. The Photoelectric Equation Work function

  8. 12-2Compton Effect

  9. 康普吞效應實驗圖表

  10. 康普吞效應圖示

  11. Energy and momentum conservation

  12. Frequency shift Compton wavelength

  13. 12-3Light as a Probability Wave The standard version

  14. The Single-Photon VersionFirst by Taylor in 1909 The single-photon, double-slit experiment is a phenomenon which is impossible, absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics - Richard Feynman

  15. The Single-Photon, Wide-Angle Version (1992) 50μm

  16. The postulate • Light is generated in the source as photons • Light is absorbed in the detector as photons • Light travels between source and detector as a probability wave

  17. 12-4Electrons and Matter Waves • The de Broglie wave length • Experimental verification in 1927 • Iodine molecule beam in 1994

  18. 1989 double-slit experiment7,100,3000, 20,000 and 70,000 electrons

  19. Experimental Verifications Electron beam X-ray

  20. 苯環的中子繞射

  21. 12-5Schrodinger’s Equation • Matter waves and the wave function • The probability (per unit time) is  Complex conjugate 共軛複數

  22. The Schrodinger Equation from A Simple Wave Function (1D)

  23. 1D Time-independent SE

  24. 3D Time-dependent SE

  25. 12-6Waves on Strings and Matter Waves

  26. 駐波與量子化 Quantization Confinement of a Wave leads to Quantization – discrete states and discrete energies 駐波：

  27. 12-7Trapping an Electron For a string：

  28. Finding the Quantized Energies of an infinitely deep potential energy well

  29. The Energy Levels 能階 • The ground state and excited states • The Zero-Point Energy n can’t be 0

  30. The Wave Function and Probability Density For a string

  31. The Probability Density

  32. Correspondence principle(對應原理) • Normalization (歸一化) At large enough quantum numbers, the predictions of quantum mechanics merge smoothly with those of classical physics

  33. A Finite Well 有限位能井

  34. The probability densities and energy levels

  35. Barrier Tunneling穿隧效應 • Transmission coefficient

  36. STM 掃描式穿隧顯微鏡 Piezoelectricity of quartz

  37. 12-8Three Electron Traps • Nanocrystallites硒化鎘奈米晶粒 • 那種顏色的顆粒比較小

  38. A Quantum Dot An Artificial Atom The number of electrons can be controlled

  39. Quantum Corral量子圍欄

  40. 12-1.9The Hydrogen Atom • The Energies

  41. The Bohr Model of the Hydrogen Atom Fig. 39-16 Balmer’s empirical (based only on observation) formula on absorption/emission of visible light for H • Bohr’s assumptions to explain Balmer formula • Electron orbits nucleus • The magnitude of the electron’s angular momentum L is quantized 39-

  42. Orbital Radius is Quantized in the Bohr Model Coulomb force attracting electron toward nucleus Quantize angular momentum l : Substitute v into force equation: Where the smallest possible orbital radius (n=1) is called the Bohr radius a: 39-

  43. Orbital Energy is Quantized The total mechanical energy of the electron in H is: Solving the F=ma equation for mv2 and substituting into the energy equation above: Substituting the quantized form for r: 39-

  44. Energy Changes Substituting f=c/l and using the energies En allowed for H: Where the Rydberg constant This is precisely the formula Balmer used to model experimental emission and absorption measurements in hydrogen! However, the premise that the electron orbits the nucleus is incorrect! Must treat electron as matter wave. 39-

  45. 氫原子能階與光譜線

  46. Fig. 39-17 Schrödinger’s Equation and the Hydrogen Atom

  47. The Ground State Wave Function

  48. Quantum Numbers for the Hydrogen Atom For ground state, since n=1→ l=0 and ml=0

  49. The Ground State Dot Plot

  50. Wave Function of the Hydrogen Atom’s Ground State Fig. 39-20 Fig. 39-21 Probability of finding electron within a within a small distance from a given radius Probability of finding electron within a small volume at a given position 39-

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