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Louis de Broglie If light, which we thought of as a wave, behaves as a particle, then maybe things we think of as particles behave as waves… photo from

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Energy/Frequency and Momentum/Wavelength Relations for a Photon Energy/Frequency and Momentum/Wavelength Relations for an Electron/Proton/Apple Pie/Ford Taurus

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What Exactly is Waving? For a photon... For a photon... –electric and magnetic fields –You can measure them if f is small enough. –For visible light, you can see that it is a wave indirectly. For a massive particle For a massive particle –You can’t measure them --- even in theory! –They are complex! –How do we know that there’s really a wave?

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How might I verify that my Ford is a wave?

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Thought Question Which of the following would be the easiest particle to use if I wanted to see a matter- wave diffraction pattern? A.A car moving at 100 mph B.A car moving at 1 mph C.A 1 MeV electron D.A 10 eV electron E.What was the question?

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Wavelength of a Ford

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Wavelength of a 10 eV Electron

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Davisson and Germer photo from

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Cesium Interferometer

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Interference of BEC

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C 60 Interference Interference fringes! The interfering particle: Buckyballs Apparatus Recent results from Vienna group of Anton Zielinger: Not only more mass, but more degrees of freedom too!

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Pure Sine Wave y=sin(5 x) Power Spectrum

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“Shuttered” Sine Wave y=sin(5 x)*shutter(x) Power Spectrum

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“Thin” Gaussian y=exp(-(x/0.2)^2) Power Spectrum

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“Fat” Gaussian y=exp(-(x/2)^2) Power Spectrum

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Femtosecond Laser Pulse E t=0 =sin(10 x)*exp(-x^2) Power Spectrum

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Uncertainty in a Classical Wave

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Uncertainty Relations Classical Wave Position – Momentum Energy – Time

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Wave-Particle Duality Things act as wave when propagating Things act as wave when propagating –or, in other words, we use waves to make predictions as to what we will find when we make our measurement. Things act as waves when we measure wave- like properties. Things act as waves when we measure wave- like properties. Things act as particles when we measure particle-like properties Things act as particles when we measure particle-like properties Example: BEC interference --- theorists confused about “undefined phase” Example: BEC interference --- theorists confused about “undefined phase”

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WHERE CAN YOU FIND TRUTH? A ride with a tow truck driver A ride with a tow truck driver An article on idiots filled with... the word An article on idiots filled with... the word Peer reviewers trying to sound smart Peer reviewers trying to sound smart A Buddhist Sunday school teacher A Buddhist Sunday school teacher

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WHERE CAN YOU FIND TRUTH? "We believe in all truth, no matter to what subject it may refer. No sect or religious denomination [or, I may say, no searcher of truth] in the world possesses a single principle of truth that we do not accept or that we will reject. We are willing to receive all truth, from whatever source it may come; for truth will stand, truth will endure." -- Joseph F. Smith

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What is stuff made of?

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Rutherford’s Experiment Shooting bullets at jello...

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Radiating Atoms

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Bohr’s Theory

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Hydrogen

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Balmer series— An electron falls to the n=2 energy state and a photon is emitted. n=6 to n=2 410 nm Violet n=5 to n=2 434 nm Violet n=4 to n=2 486 nm Bluegreen n=3 to n=2 656 nm Red Balmer series— An electron falls to the n=2 energy state and a photon is emitted. n=6 to n=2 410 nm Violet n=5 to n=2 434 nm Violet n=4 to n=2 486 nm Bluegreen n=3 to n=2 656 nm Red

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An electron absorbs a photon and jumps to a higher energy level.

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The green emission line in hydrogen is a transition from an excited state n=4 to n=2. The red line must be a transition from ______ to n=2. A. n=1 B. n=2 C. n=3 D. n=4 E. n=5

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Which transition in hydrogen gives off the shortest wavelength (highest energy) of radiation. A. n=2 to n=1 B. n=3 to n=2 C. n=6 to n=3 D. n=8 to n=4 E. n=100 to n=5

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Bohr Theory Successes/Failures ☺ Predicts emission and absorption lines of hydrogen and hydrogen-like ions ☺ Predicts x-ray emissions (Moseley’s law) ☺ Gives an intuitive picture of what goes on in an atom ☺ The correspondence principle is obeyed... sort of X It can’t easily be extended to more complicated atoms X No prediction of rates, linewidths, or line strengths X Fine structure (and hyperfine structure) not accounted for X How do atoms form molecules/solids? X Where did it come from? There must be a more general underlying theory! ☺ It gave hints of a new, underlying theory

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Schorodinger’s Idea Probability waves Probability waves –Tells the probability of finding a particle at some particular place at a particular time. –The electron is more likely to be where the amplitude of the wave is high.

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Match the spectrum to the one you see. HHeONe

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Tunneling

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Cross-section of a MOSFET transistor gate consisting of a 2 nm thick amorphous silicon oxide layer between crystalline silicon (top) and polycrystalline silicon (bottom). Individual atomic columns and dumbbells are clearly visible. The image provides data on the precise location and roughness of the gate oxide interface, while revealing how the silicon crystal structure is locally affected near the interface. (Source: FEI Co.)

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STM image

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STM image

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STM image

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Postulates of Quantum Mechanics Every physically-realizable system is described by a state function ψ that contains all accessible physical information about the system in that state Every physically-realizable system is described by a state function ψ that contains all accessible physical information about the system in that state The probability of finding a system within the volume dv at time t is equal to |ψ| 2 dv The probability of finding a system within the volume dv at time t is equal to |ψ| 2 dv Every observable is represented by an operator which is used to obtain information about the observable from the state function Every observable is represented by an operator which is used to obtain information about the observable from the state function The time evolution of a state function is determined by Schrödinger’s Equation The time evolution of a state function is determined by Schrödinger’s Equation

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