Chapter 29 Particles and Waves by qjk18715

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									                                                                                                                                                                  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


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                                                                                                                                                               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




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                                           Solvay conference, 1927                                                                                                                              Solvay conference, 1927
                                           Solvay conference, 1927                                                                                                                              Solvay conference, 1927
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                                                                                                                                                                                                                                                          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#

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                                                                                                                  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?)

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                                                                                                            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.

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