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UCSD PHYS 10 - Quantum Mechanics

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Quantum MechanicsThe Quantum Mechanics ViewCrises in physics that demanded Q.M.Pre-quantum problems, cont.Problems, cont.The victory of the weird theoryLet’s start with photon energyHow come I’ve never seen a photon?Quantum WavelengthThe Uncertainty PrincipleExample: DiffractionDiffraction in Our Everyday WorldThe Double Slit ExperimentResultsWave or Particle? Neither; Both; take your pickThe hydrogen atomThe angular part of the storyPowerPoint PresentationAssignmentsUCSDPhysics 10Quantum MechanicsQuantum MechanicsSmall things are weirdSmall things are weirdSpring 2008 2UCSDPhysics 10The Quantum Mechanics ViewThe Quantum Mechanics View•All matter (particles) has wave-like propertiesAll matter (particles) has wave-like properties–so-called particle-wave duality•Particle-waves are described in a probabilistic mannerParticle-waves are described in a probabilistic manner–electron doesn’t whiz around the nucleus, it has a probability distribution describing where it might be found–allows for seemingly impossible “quantum tunneling”•Some properties come in dual packages: can’t know both Some properties come in dual packages: can’t know both simultaneously to arbitrary precisionsimultaneously to arbitrary precision–called the Heisenberg Uncertainty Principle–not simply a matter of measurement precision–position/momentum and energy/time are example pairs•The act of “measurement” fundamentally alters the systemThe act of “measurement” fundamentally alters the system–called entanglement: information exchange alters a particle’s stateSpring 2008 3UCSDPhysics 10Crises in physics that demanded Q.M.Crises in physics that demanded Q.M.•Why don’t atoms disintegrate in nanoseconds?Why don’t atoms disintegrate in nanoseconds?–if electron is “orbiting”, it’s accelerating (wiggling)–wiggling charges emit electromagnetic radiation (energy)–loss of energy would cause prompt decay of orbit•Why don’t hot objects emit more ultraviolet Why don’t hot objects emit more ultraviolet light than they do?light than they do?–classical theory suggested a “UV catastrophe,” leading to obviously nonsensical infinite energy radiating from hot body –Max Planck solved this problem by postulating light quanta (now often called the father of quantum mechanics)Spring 2008 4UCSDPhysics 10Pre-quantum problems, cont.Pre-quantum problems, cont.•Why was red light incapable of knocking electrons out of certain Why was red light incapable of knocking electrons out of certain materials, no matter how brightmaterials, no matter how bright–yet blue light could readily do so even at modest intensities–called the photoelectric effect–Einstein explained in terms of photons, and won Nobel PrizeSpring 2008 5UCSDPhysics 10Problems, cont.Problems, cont.•What caused spectra of atoms to What caused spectra of atoms to contain discrete “lines”contain discrete “lines”–it was apparent that only a small set of optical frequencies (wavelengths) could be emitted or absorbed by atoms•Each atom has a distinct “fingerprint”Each atom has a distinct “fingerprint”•Light only comes off at very specific Light only comes off at very specific wavelengthswavelengths–or frequencies–or energies•Note that hydrogen (bottom), with Note that hydrogen (bottom), with only one electron and one proton, only one electron and one proton, emits several wavelengthsemits several wavelengthsSpring 2008 6UCSDPhysics 10The victory of the weird theoryThe victory of the weird theory•Without Quantum Mechanics, we could never have Without Quantum Mechanics, we could never have designed and built:designed and built:–semiconductor devices•computers, cell phones, etc.–lasers•CD/DVD players, bar-code scanners, surgical applications –MRI (magnetic resonance imaging) technology–nuclear reactors–atomic clocks (e.g., GPS navigation)•Physicists didn’t embrace quantum mechanics because it Physicists didn’t embrace quantum mechanics because it was gnarly, novel, or weirdwas gnarly, novel, or weird–it’s simply that the #$!&@ thing worked so wellSpring 2008 7UCSDPhysics 10Let’s start with photon energyLet’s start with photon energy•Light is Light is quantizedquantized into packets called into packets called photonsphotons•Photons have associated:Photons have associated:–frequency,  (nu)–wavelength,  ( = c)–speed, c (always)–energy: E = h•higher frequency photons  higher energy  more damaging–momentum: p = h/c•The constant, The constant, hh, is Planck’s constant, is Planck’s constant–has tiny value of: h = 6.6310-34 J·sSpring 2008 8UCSDPhysics 10How come How come I’veI’ve never seen a photon? never seen a photon?•Sunny day (outdoors):Sunny day (outdoors):–1015 photons per second enter eye (2 mm pupil)•Moonlit night (outdoors):Moonlit night (outdoors):–51010 photons/sec (6 mm pupil)•Moonless night (clear, starry sky)Moonless night (clear, starry sky)–108 photons/sec (6 mm pupil)•Light from dimmest naked eye star (mag 6.5):Light from dimmest naked eye star (mag 6.5):–1000 photons/sec entering eye–integration time of eye is about 1/8 sec  100 photon threshold signal levelSpring 2008 9UCSDPhysics 10Quantum WavelengthQuantum Wavelength•Every particle or system of particles Every particle or system of particles cancan be defined in be defined in quantum mechanical termsquantum mechanical terms–and therefore have wave-like properties•The quantum wavelength of an object is:The quantum wavelength of an object is: = h/p (p is momentum)–called the de Broglie wavelength•typical macroscopic objectstypical macroscopic objects–masses ~ kg; velocities ~ m/s  p  1 kg·m/s  10-34 meters (too small to matter in macro environment!!)•typical “quantum” objects:typical “quantum” objects:–electron (10-30 kg) at thermal velocity (105 m/s)    10-8 m–so  is 100 times larger than an atom: very relevant to an electron!Spring 2008 10UCSDPhysics 10The Uncertainty PrincipleThe Uncertainty Principle•The process of measurement involves interactionThe process of measurement involves interaction–this interaction necessarily “touches” the subject–by “touch,” we could mean by a photon of light•The more precisely we want to know where something is, The more precisely we want to know where something is, the “harder” we have to


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UCSD PHYS 10 - Quantum Mechanics

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