Physics of Technology PHYS 1800

1. Physics of TechnologyPHYS 1800 Lecture 37 Quantum Mechanics in a Day

2. PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet *Homework Handout

3. Interference • Young’s Double Slit experiment You must add amplitudes E, not powers P (intensities)

4. Interference of Light Waves Is light a wave or a particle? • If it is a wave, it should exhibit interference effects: Recall that two waves can interfere constructively or destructively depending on their phase.

5. Light from a single slit is split by passing through two slits, resulting in two light waves in phase with each other. • The two waves will interfere constructively or destructively, depending on a difference in the path length. • If the two waves travel equal distances to the screen, they interfere constructively and a bright spot or line is seen.

6. If the distances traveled differ by half a wavelength, the two waves interfere destructively and a dark spot or line appears on the screen. • If the distances traveled differ by a full wavelength, the two waves interfere constructively again resulting in another bright spot or line. • The resulting interference pattern of alternating bright and dark lines is a fringe pattern.

7. Similarly, interference can occur when light waves are reflected from the top and bottom surfaces of a soap film or oil slick. • The difference in the path length of the two waves can produce an interference pattern. • This is called • thin-film • interference.

8. Different wavelengths of light interfere constructively or destructively as the thickness of the film varies. • This results in the many different colors seen.

9. The thin film may also be air between two glass plates. • Each band represents a different thickness of film.

10. Diffraction and Gratings • The bright fringes in a double-slit interference pattern are not all equally bright. • They become less bright farther from the center. • They seem to fade in and out. • This effect, called diffraction, is due to interference of light coming from different parts of the same slit or opening.

11. Diffraction • For constructive interference:

12. The diffraction pattern produced by a square opening has an array of bright spots. • Looking at a star or distant street light through a window screen can produce a similar diffraction pattern.

13. X-Ray Diffraction Braggs’s Law: nλ=2d sin(Θ)

14. Why study everyday phenomena? • The same physical principles that govern our everyday experiences also govern the entire universe • A bicycle wheel, an atom, and a galaxy all operate according to laws for angular momentum.

15. What are the major subfields in Physics? • Classical Physics(pre 20th century) • Mechanics → forces, motion • Thermodynamics → heat, temperature • Electricity and magnetism → charge, currents • Optics → light, lenses, telescopes • Modern Physics (20th century) • Atomic and nuclear → radioactivity, atomic power • Quantum mechanics }→ basic structure matter • Particle physics • Condensed matter → solids and liquids, computers, lasers • Relativity, Cosmology → universe, life!

16. State of Physics cira 1895 • Conservation Laws • Energy • Linear & Angular Momentum • Statistical Mechanics • 3 Laws of Thermodynamics • Kinetic Theory

17. Limits of pre-Modern Physics

18. Then All Hell Broke Lose“Thirty Years That Shook Physics” • 1887 Michelson-Morley exp. debunks “ether” • 1895 Rontgen discovers x rays • 1897 Becquerel discovers radioactivity • 1897 Thomson discovers the electron • 1900 Planck proposes energy quantization • 1905 Einstein proposes special relativity • 1915 Einstein proposes general relativity • 1911 Rutherford discovers the nucleus • 1911 Braggs and von Laue use x rays to determine crystal structures • 1911 Ones finds superconductors • 1913 Bohr uses QM to explain hydrogen spectrum • 1923 Compton demonstrates particle nature of light • 1923 de Broglie proposes matter waves • 1925 Davisson & Germer prove matter is wavelike • 1925 Heisenberg states uncertainty principle • 1926 Schrodinger develops wave equation • 1924-6 Boson and Fermion distributions developed • 1949 Murphy's Law stated

19. Current State of Physics cira 2009 • Conservation Laws • Energy • Linear & Angular Momentum • Charge, Spin • Lepton and Baryon Number • Statistical Mechanics • Physics of many particles • Fermions and Bosons • Partitioning of Energy • Thermodynamics • Time and Entropy • Weinburg-Salom Model • QED • Unites E&M, Weak NF • Quantum Mechanics • Schrodinger/Dirac Equation • Probabilistic approach

20. Limits of Current Modern Physics

21. Cathode rays, Electrons, and X-rays • By the end of the nineteenth century, chemists were using the concept of atoms to explain their properties. • Physicists were less convinced. • The discovery of cathode rays was the beginning of atomic physics. • Two electrodes are sealed in a glass tube. • As the tube is evacuated, a glow discharge appears in the gas between the electrodes. • With further evacuation, the discharge disappears, and a glow appears on the end of the tube opposite the cathode.

22. An invisible radiation seemed to emanate from the cathode to produce the glow on the opposite wall of the tube. • The invisible radiation was called cathode rays. • If the north pole of a magnet is brought down toward the top of a cathode-ray tube, the spot of light is deflected to the left across the face of the tube. • This indicates the cathode rays are negatively charged particles. • Two electrodes are sealed in a glass tube. • As the tube is evacuated, a glow discharge appears in the gas between the electrodes. • With further evacuation, the discharge disappears, and a glow appears on the end of the tube opposite the cathode.

23. J. J. Thomsonused both electric fields and magnetic fields to deflect the beam. • The combined effect allowed him to estimate the velocity of the particles. • With the deflection produced by the magnetic field alone, this allowed him to estimate the mass of the particles. • We now call these particles electrons.

24. You probably use cathode rays almost every day. • The heart of most television sets is the cathode ray tube, or CRT. Do you know how a TV works?

25. The electrodes that produce and focus the electron beam are called the electron gun. • An electric current passes through the filament to heat the cathode to emit electrons. • Electrons are accelerated from the cathode to the anode by the high voltage. • Electrons passing through the hole in the anode make up the electron beam. • After leaving the electron gun, the beam of electrons travel across the tube, producing a bright spot of light when it strikes the glass face of the tube. • Magnets deflect the beam so that it strikes different points on the face of the tube at different times. • The beam scans across the entire face of the tube in a fraction of a second, to form the picture.

26. Experiments on the “New”Particle”The Electron Robert Millikan measured the quantized charge on the electron J.J. Thomson measured the charge-to-mass ratio e/m

27. In 1927 Davisson and Germer first demonstrated the diffraction patterns generated by electrons of 10eV passing through a Ni crystal. Davisson and Germer Experiment For electrons:

28. Electron Diffraction Energy Electron Diffraction: Electron and x-ray both exhibit diffraction from crystals. Braggs’s Law: nλ=2d sin(Θ)

29. Electron Interference Electron Single Slit Interference: Effects are clearly observed. However, as soon as “electron tracking” is instituted, the interference pattern disappears!

30. Low Energy Electron Diffraction Typical LEED systems. (left) UHV surface analysis chamber. (right) LEED electron guns and grids. Low Energy Electron Diffraction is a standard tool in surface science. ~50 eV electrons with λ~1 Å are diffracted from surface atoms to determine atomic structure.

31. LEED Images A SPA LEED image of silicon taken with 128 eV electrons. The organic molecule PTCDI adsorbed on the 110 surface of Ag.

32. Neutron Diffraction (left) Triple axis neutron diffractometer at the NIST Neutron scattering facility. (right) Diffraction pattern from nuetrons.

33. ...even Quantum Physics (matter waves)...

34. Nobel Prizes Related to Wave-Particle Duality • There have been 14 Nobel Prizes in physics awarded that have some direct relation to the wave-particle duality. Albert Einstein received the Nobel Prize for one of these, the photoelectric effect. • Annotated list of winners.

35. Pioneers in the Wave Theory of Particles Born Heisenburg Schrodinger

36. In 1924 de Broglie suggested that electrons may have wave properties. The wave length of an electron is proposed to be h/p where p is the momentum of the electron. Particles as a Wave De Broglie waves: • This expression is consistent with photon (E=pc) or p=h/ λ. • Because of the Planck constant, the λ of macroscopic object is not detectable. • Lower momentum particle is more wavelike. • Higher energy wave is more particle like. For electrons:

37. Assume the mass of the jelly bean is 5 g and its velocity is 1 m/s. The total energy is just the kinetic energy E=KE=1/2 mv2 . De Broglie Wave Problems What is the de wave length of a jelly bean? Then And What is the de Broglie wave length of a Germer electron? For an electron all the electrostatic PE is converted to KE, eV  1/2 mv2 . First solve for p then for λ. First Then

38. Waves of what? • The physical interpretation of de Broglie waves (the wave function or Schrodinger waves) is related to the probability of finding a moving particle at a particular location (x,y,z) and time t. • Because Ψ(x,y,z,t) is complex and can be positive or negative, it cannot be the probability directly. • | Ψ(x,y,z,t) |2 is the probabilityof finding the particle at location (x,y,z) at time t. • To be a probability function, it must obey a normalization condition stating it must be somewhere: Born Schrodinger

39. must be continuous The Schrödinger Equation The Schrodinger Wave equation: U(x): Potential Energy Complex wave function probability to find the particle at (x,t) normalization of the wave function Let Time independent Schrödinger equation

40. Matter is made up of atoms… • The Atomic Theory, a cornerstone of modern science, was proposed by an early Greek thinker, Democritus (c.460 BC - c.370 BC). • 2400 year later, Feynman deemed this the most important notion in science

41. Trying to see atoms… STM Image (3,000,000 X mag) Optical image (5 X mag) SEM Image (300,000 X mag) STM Image (24,000,000 mag) Magnified images of semiconductor chip.

42. Seeing atoms…finally!!! • Atomic scale images seen with scanning tunneling microscope • STM developed in 1985 at IBM • Measures extent of electron cloud Binnig and Roher’s original STM

43. Examples of STM images… • Pt (100) with vaccancies • Si (111) 7x7 reconstruction • Annealed decanethiol film on Au(111) • Si (111) with terraces and vaccancies

44. Examples of STM images (part 2)…

45. V(x) V0 E 0 a x Barrier Penetration (QuantumTunneling) Ψ is damped Ψ oscillates There is a certain probability T that the particle can tunnel through the barrier, where The thicker or higher the barrier, the less the tunneling probability  approaches classical result

46. How an STM works… • An STM s a glorified phonograph needle • Tip motion uses piezioelectric crystals • Tunneling current results from overlap of electron wavefunction with conducting surface

47. How an STM works (part 2)…

48. Corralling electrons… STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.

49. Corralling electrons… STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.

50. Corralling electrons… STM used to make direct maps of the Quantum Mechanicsl probability distribution of the electron wave function of 2D state confined by “corrals” made of adsorbed atoms.