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Anyone Who Is Not Shocked by Quantum Theory Has Not Understood It."—Niels Bohr

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"Anyone who is not shocked by quantum theory has not understood it."—Niels Bohr “I think I can safely say that nobody understands quantum mechanics."—Richard Feynman Inside the Quantum World Science's most precise and influential tool Particles and waves, and their interactions and interrelationships Atoms, molecules and material structure Atomic, nuclear, particle, and condensed matter physics, chemistry, biology, information and communication technology... Quantum Theory or Science (“Quantum Mechanics” is Imprecise) ● Probably the most successful of all scientific theories (in terms of the accuracy and breadth of its predictions, and its impact) – Calculations of the fine structure constant, α, within the context of quantum electrodynamics, agree with experiment to 0.32 parts per billion – Applications: transistor, laser, semiconductors, integrated circuits, diagnostics, optical communications, clocks, computers.... Fluorescing Ions in a Linear Trap Thirty-two ions, fluorescing under illumination by laser light in an electrodynamic trap Annenberg Foundation 2013. All rights reserved. Ultra-Cold Atoms Trapped in Standing Light Waves Neutral rubidium atoms in an optical lattice trap Annenberg Foundation 2013. All rights reserved. Newton Wasn't Perfect ● Didn't know high speeds or really small objects ● The Calculus is premised on continuous distributions ● On the microscopic level, nature is – quantized: separated into discrete quantities But he did claim that light was composed of particles... Newton's Particle Theory of Light ● Little particles, so tiny they (intersecting beams, for example) don't scatter one another ● Obey the same laws of physics as all other objects Foucault's Light Speed Experiment Young's Double Slit Experiment Young's Double Slit Experiment Arago/Poisson Spot Diffraction and Interference © Eli Sidman, Technical Services Group, MIT. Single Slit ~ 2 Wavelengths Wide © Eli Sidman, Technical Services Group, MIT. Small Single Slit (top) Many Small Slits (bottom) Photoelectric Effect If Light Were a Wave... ● Electron ejection rate proportional to intensity ● But at very low intensity, emission delayed ● Maybe some rate dependence on frequency ● Maximum kinetic energy of emitted electrons probably related to intensity and maybe frequency The Experiment Homework http://phet.colorado.edu/en/simulation/photoelectric The Results ● Current always directly proportional to intensity—even down to the lowest intensities – “...no indication whatsoever of … a threshold... intensity” – Also, no measurable time delay even at lowest intensities ● The stopping potential unaffected by intensity, only by color (frequency, wavelength) – Maximum kinetic energy unaffected by intensity The Interpretation (Einstein 1905) ● Electromagnetic radiation created by vibrating charged particles ● Particle energies are quantized ● Emitted radiation therefore quantized ● Quanton of radiation is called a photon. What is a Wave? ● A wave is a periodic disturbance in a medium © Adam Kleppner © Annenberg Foundation 2013. ● Essential properties: – Wavelength – Frequency – Velocity – Amplitude – Interference Additional Wave Characteristics ● Energy spreads out with wave fronts ● Superposition – Waves pass freely through one another – At intersections, amplitudes add (interference) ● In constrained systems, standing waves © Eli Sidman, Technical Services Group, MIT. © Annenberg Foundation 2013. © Daniel Kleppner. Wave Theory of Electromagnetic Radiation (Maxwell) ● Oscillations between electric and magnetic fields which spread according to a wave equation ● Can be reflected, refracted, polarized, and (most importantly) diffracted ● All travel at same speed, c What is a Particle? ● A particle is an object of negligible size ● Essential properties: – Mass – Momentum – (Kinetic) Energy “Particle” Theory of Electromagnetic Radiation (Einstein) ● Consists of bundles of energy called photons ● Photon energy is proportional to the frequency – The proportionality constant is called Planck's constant, h ● Being relativistic, photons carry moment = energy/c – Mechanical waves possess energy, but they carry no momentum Interference pattern built up photon by photon Paradox ● Light exhibits all the behaviors predicted by Maxwell's wave theory of electromagnetic radiation (many of which particles do not exhibit) ● Einstein's particle-like energy bundles completely explain the photoelectric effect (wave theory doesn't) [ 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. In reality, it contains the only mystery. We cannot make the mystery go away by explaining how it works. — Richard Feynman Single Photon Double Slit Experiment Matter ● Ordinary matter consists of atoms ● There are a finite number of different atoms (elements) – Each type exhibits a unique pattern of radiated or absorbed wavelengths The Atom Consists of a central nucleus surrounded by clouds of electrons How the Cathode Ray Tube Works Cathode Ray Tube ● Different gases produced different colored discharges ● Reduced pressure halts discharges and darkens tube except for a glow around the anode and florescence of the glass Crookes's Tube Cathode rays travel in straight lines Originate at cathode and carry energy and momentum Carry negative charge J.J. Thomson Measures charge/mass Thomson's Results ● Ratio the same regardless of accelerating voltage ● Ratio the same regardless of cathode material ● Ratio 1836 times bigger than that of hydrogen ions ● The atom is not the smallest smallest object Note: Philipp Lenard detected cathode rays passing undeflected through thin metal foil and concluded that they must be waves; charged objects would have to scatter (if it couldn't be a particle it had to be a wave) Discovering a New Object ● Something with a definite charge/mass ratio ● Something found in cathode rays and photoelectric ejection ● Something ejected from elements under the influence of X-rays ● … A particle called an electron: a small, light, negatively charged component of all atoms Waves Through a Single Slit Particles Through a Single Slit Waves Through a Double Slit Particles Through a Double Slit? Single Electron Double Slit Experiment 700,000 Electrons Shot One at a Time Louis de Broglie (1924) “Following Einstein's introduction of photons in light waves, one knew that light contains particles which are concentrations of energy incorporated into the wave, suggests that all particles, like the electron, must be transported by a wave into which it is incorporated... My essential idea was to extend to all particles the coexistence of waves and particles discovered by Einstein in 1905 in the case of light and photons." “Wave-Particle Duality” ● Identically prepared particles impact in an extended pattern – Different particles impact at different points – Impact point of any particular particle is uncertain ● The overall pattern is reproducible and predictable Wave-Particle Duality in the Double Slit Experiment Erwin Schrödinger (1925) ● Take the wave nature of matter as fact and determine: – How do matter waves behave? – What do we mean by a matter wave? ● Wave Mechanics – Wave equations for particles psi Werner Heisenberg (1926) ● Matrix Mechanics = Wavefunction = Psi Field ● A particular solution to Schrödinger's equation ● The magnitude squared is a probability distribution ● Predict the range for the result of a measurement, not the exact value ● Penetrates into classically forbidden regions: tunneling – If the energy barrier is not too high, a particle can pass from one classically allowed region to another through a region that is classically forbidden. Single Electrons Through Two Slits ● Each electron passes through both slits, interfering with itself, before interacting with the screen at one point Particle in a Box ● Confined system quantized energies ● Smooth transition at boundaries integral half-wavelength solutions ● Energy increases as Harmonic Oscillator © Daniel Kleppner. ● Confined energies quantized ● Energy proportional to frequency ● Energy increases linearly as n Psi Field (Wavefunction) ● Field: assign one or more values to every point in space(time) ● Square of psi field assigns a probability to every point in space(time) Harmonic Oscillator n=0 Harmonic Oscillator n=10 Correspondence Principle The transition between quantum and classical worlds should be smooth: in the limit of large energy state quantum numbers, atomic systems should display classical-like behavior Spectroscopy ● Measurement of the absorption, scattering, or emission of electromagnetic radiation by atoms or molecules ● Each element (type of atom), exhibits a unique pattern (radiation or absorption line spectrum) of individual wavelengths if sufficiently excited Line Spectra ● How is it that different atoms radiate and absorb characteristic spectra? ● What does this tell us about the structure of atoms? The Nuclear Atom (1905) ● Rutherford determines that most of the mass of an atom is located in a tiny volume—the nucleus—at the center of the atom ● Planetary model of the atom ● But accelerating charges radiate: electrons should spiral into nucleus, emitting ever higher frequency light—spectrum should be broad, not sharp ● Atoms would collapse in very little time Bohr Model (1913) ● Hydrogen atoms exist in certain fixed energy states (stationary states), labeled by a quantum number ● “Jumping” between energy states involves absorbing or emitting radiation
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