VIEWS: 0 PAGES: 7 CATEGORY: Debt & Credit POSTED ON: 7/20/2010
There is nothing new to be discovered in physics now. All that remains is Chapter 29 more and more precise measurement. Particles and Waves -- William Thomson, Lord Kelvin (Address at the British Association for the Advancement of Science, 1900). The last Mastering Physics assignment is now available. It is on material in chapters 27, 28, and 29. Due: Monday, 7 April, 11 pm 1 2 Quantum Physics The more important fundamental laws and facts of • 2nd revolution in physics: physical science have all been discovered, and these – Starts with Planck ~1900 are now so ﬁrmly established that the possibility of – Contributions from Einstein, Bohr, Heisenberg, their being supplanted in consequence of new Schrödinger, Born, Dirac, de Broglie …. over 25 years discoveries is exceedingly remote. Our future • Cornerstones: discoveries must be looked for in the sixth place of – Wave-particle duality decimals. – Uncertainty principle • Correspondence Albert Michelson (1899) – Applies for small dimensions • Planck’s constant: h = 6.6 x 10-34Js • As h -> 0, quantum physics -> classical 3 4 Solvay conference, 1927 Solvay conference, 1927 Solvay conference, 1927 Solvay conference, 1927 er g ber ing isen röd Sch He ie ton l rog mp B Co de Pauli Born Bohr Bragg Dirac Planck Curie Lorentz Einstein Front row: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A. Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson, O. W. Richardson. Second Front row: I. Langmuir, M. Planck, M. Curie, H. A. Lorentz, A. Einstein, P. Langevin, C. E. Guye, C. T. R. Wilson, O. W. Richardson. Second row: P. Debye, M. Knudsen, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compton, L. V. de Broglie, M. Born, N. Bohr. Standing: A. row: P. Debye, M. Knudsen, W. L. Bragg, H. A. Kramers, P. A. M. Dirac, A. H. Compton, L. V. de Broglie, M. Born, N. Bohr. Standing: A. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin. Piccard, E. Henriot, P. Ehrenfest, E. Herzen, T. De Donder, E. Schroedinger, E. Verschaffelt, W. Pauli, W. Heisenberg, R. H. Fowler, L. Brillouin. 5 6 1) Blackbody radiation a) Blackbody • All objects radiate and absorb electromagnetic radiation Part I: Particle nature of light • At equilibrium, rate of absorption = rate of emission • Best absorber is best emitter – Perfect absorber is perfect emitter Cavity is model of a perfect blackbody 7 8 b) Emmitance spectrum: the problem Theory Plot of intensity vs wavelength Classical prediction: – Depends only on temperature The UV catastrophe Experimental spectrum: • All oscillations equally probable • More oscillations possible at lower wavelength Violates common sense and experiment 9 10 c) Energy quantization: the solution Absorption and emission occur in discrete quanta only d) Planck’s constant, h Energy of quanta proportional to frequency E = nhf = hc / !; n = 0,1,2,3... c E = nhf = nh ; n = 0,1, 2, 3... ! • Planck found a “fudge factor” by “happy guesswork” to make For small wavelength (high freq), quanta are large. the experiment ﬁt. He developed a quantization theory to predict the value h. If kT (thermal energy) < quantum, radiation not possible. – “lucky artifact of more fundamental reality yet to be discovered” h = 6.626 ! 10 "34 Js • Nobel prize, 1918 11 12 2) Photoelectric effect b) Expectations and observations a) The effect Experiment Expectation Observation Increase intensity - Max energy increase - Max energy constant - Current increase - Current increase - Time lag decrease - No time lag Increase Frequency - Max energy constant - No threshold 13 14 Observed frequency dependence b) Expectations and observations Experiment Expectation Observation Increase intensity - Max energy increase - Max energy constant - Current increase - Current increase - Time lag decrease - No time lag Increase Frequency - Max energy constant - Max energy prop to freq - No threshold - Threshold frequency characteristic of metal 15 16 c) Einstein theory KEmax = hf - W0 • Found same value for h as Planck had Energy of photon Work required to • Nobel prize in 1921 (from Planck) remove electron • In 1913, Planck recommended Einstein for membership in the Prussian Academy. “Notwithstanding his genius, he may sometimes have missed the target in his speculations, as, for example, in his hypothesis of light quanta.” 17 18 3) The Compton Effect, 1923 b) The experiment a) The effect: Scattering of x-ray by X-ray source (") electron changes the wavelength Crystal ! graphite Detector Bragg reﬂection gives "’ 19 20 c) Classical prediction d) Compton’s explanation - Conservation of energy: hf = hf ! + KE - incident wave excites electron at frequency f ! ! ! - Conservation of Momentum: p = p! + pe E hf h ! - electron radiates at frequency f - Energy-momentum relation for light: p= = = c c ! Combining these equations gives: h " "! # " = (1# cos $ ) mc "’ Nobel prize, 1928 Deﬁnitive evidence for photons 21 22 Wave-particle duality of light: Light interacts with matter like particles (photoelectric effect, blackbody radiation, Compton scattering). Light propogates like waves (interference, diffraction). Part II: The wave nature of particles 23 24 4) The de Broglie wavelength, 1924 a) The hypothesis The idea that electrons were wavelike, just as light was particle-like, The dual nature observed in light is present in brought at pleasing symmetry to nature. matter: This speculation was the basis de Broglie’s PhD thesis, submitted in E = hf = hc / ! } A photon has energy h != Paris. From electromagnetism, E = pc p The concept was considered outlandish, and a copy was sent to By analogy, de Broglie proposed that a particle with momentum p Einstein for his opinion. The great man was enthusiastically is associated with a wave with wavelength: supportive, and the degree was promptly granted. h Siz years later (1929), de Broglie received the Nobel prize. != p 25 26 b) Electron diffraction/interference - Davisson & Germer observed electron diffraction by accident in 1926 - GP Thomson observed it deliberately (and independently) in 1927 - In 1937, Davisson & Thomson shared the Nobel prize for electron diffraction - (JJ Thomson won in 1906 for discovery of electron as a particle; his son won 30 years later for discovery of the electron as a wave) 27 28 Electron microscope image of a spruce aphid 5) The Heisenberg Uncertainty Principle The wave nature of particles means that position and momentum (wavelength) cannot simultaneously be determined to arbitrary accuracy. The smaller the slit above, the better the y-position is known, but the greater the spread in y-momentum. 29 30 The principle applies separately to any 6) Interpretation component of momentum and position: Waves and particles propagate and interfere like waves, but interact like particles. h !py !y " Copenhagen Interpretation: 4# A physical state (photon, electron, system) is described by a h wave function (#), which propagates according to physical !px !x " 4# laws (Schrödinger’s equation) (and can interfere). The intensity of particle’s wave represents the probability of observing the particle at that location. and to energy and time: A system (particle) is said to be in a superposition of all h possible states, until a measurement “collapses” the wave !E!t " function to a single possible state. 4# 31 32 In any physical theory, one must distinguish the concepts that are physically observable from those which are not. The former must of necessity play a role in the theory, the latter can be modiﬁed or abandoned without impairment. • Pattern observed, even for low ﬂux (one electron at a time) • Which slit does it go through? • Experiments to determine the answer, wipe out the pattern. • Is reality independent of observation? If a tree falls in the forest... (Are there hidden variables?) 33 34 Schrödinger’s Cat One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter The whole idea of quantum jumps there is a tiny bit of radioactive substance, so small, necessarily leads to nonsense. … If we that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, are still going to have to put up with perhaps none; if it happens, the counter tube these damn quantum jumps, I am sorry discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If that I ever had anything to do with one has left this entire system to itself for an hour, quantum theory. one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or Erwin Schrödinger smeared out in equal parts. 35 36 God does not play dice with the universe Einstein I think I can safely say that nobody understands Stop telling God what to do quantum mechanics. Neils Bohr Doesn’t this marvelous discovery make you willing to Richard Feynman, The Character of accept the quantum theory, Professor Einstein?” He Physical Law, 1967 replied in a serious voice, “I still cannot believe that God plays dice. But maybe”, he smiled, “I have What I am going to tell you about is what we teach earned the right to make my mistakes.” our physics students in the third or fourth year of graduate school... It is my task to convince you not to turn away because you don't understand it. You John Wheeler, in reference to Feynman’s theory see my physics students don't understand it. ... That (1941) is because I don't understand it. Nobody does. (Feynman, Richard P. Nobel Lecture, 1966, 1918-1988, QED, The Strange Theory of Light and Matter) And yet, quantum mechanics is spectacularly successful at predicting the outcome of experiments performed at distance scales spanning many orders of magnitude. 37 38