I hear a train a comin’Slide 2The QuantumMasters of the UniverseTrain wrecksBlackbody radiationWhat the Masters wantedHow to make a blackbodyTurning on the lightMeasuring the Frequency as a function of temperatureSeveral FrequenciesExplaining ItThe “Ultraviolet Catastrophe”Rayleigh-Jeans LawPlanck’s IdeaWalking the Planck…PhotoElectric Effect– Einstein’s Only Nobel PrizeEinstein takes the next step…Maximum Kinetic EnergyEinstein’s wordsMillikan Corroborates This in 1916Another ObservationIn More DetailWhat is the problem?The Bohr ModelThe Bohr Model, cont’dEnergy QuantizationDerive This!HintNeed some stuff from RelativityDe Broglie and Matter WavesDe Broglie WavesDavisson, Germer, etcThe Wave FunctionThe WavefunctionConsider the following:IntensityA way out…Waves is waves….Euler AnglesHow to get rid of complex numberProbability densityNormalizing a wave functionBack to the “salad days” of Physics 270WavesMatter WavesFourier AnalysisSlide 49Making a square wave using continuous wavesFourier TransformWhat about reversing the process?A simple exampleSome NotationTime Domain to Frequency DomainConsider the following behaviorAn AsideNow, the big finishContinuing this line of reasoningNearly thereIf I use RMS uncertaintiesWe’re Not in Classical land any moreI hear a train a comin’I hear the train a comin‘ It's rollin' 'round the bend,… But that train keeps a-rollin',On down to San Antone.Johnny CashThe Quantumquantum from quantus: latin for how muchIf quantum theory had been initiated by native English-speakers at the turn of the 21st century, I suspect that they would have used the word “pixel”pixel mechanics or the physics of the energy pixel.Quantized means certain discrete amountsSynonymous with “pixillated”In this section, we will first learn about why they had to abandon classical mechanics and think about pixels of energyMasters of the UniverseOne last thing to realize, the 19th century physicists considered the picture of physics as nearly complete with no new surprises… just some loose ends to tie upI sometimes think that 21st century physicists think the same thing…Train wrecksWe will discuss three experiments which essentially “train wrecked” classical physics.I use the words “train wreck” because 19th century physics was an unstoppable locomotive with a well defined path going into the futureAnd then someone put three little coins on the rails…Blackbody radiationA “blackbody” absorbs 100% of the radiation that strikes it and emits NONE backKind of a blackhole of radiation without the nasty gravitational effectsBlacker than the nastiest t-shirt of the nastiest Goth after 3 days in the mud at Bonneroo…What the Masters wantedObservation: all materials when heated changed to a dull red color at 11000C and that color shifts toward blue as temperature increasesBy all materials, I mean EVERYTHING, metal, salt, you, me, your cat…They wanted to find an ideal black body: perfectly absorbs, perfectly emits..For 40 years, they tried to calculate the blackbody radiation pattern from 1st principlesThe practical problem was to develop a measurement standard the new-fangled “light bulb” at the German bureau of standards.How to make a blackbodyMake a box with a small holeThe radiation which enters the box is perfectly absorbed except for a small amount which exits the holeIt follows from Prévost's theory of exchanges of 1792 that the best radiation absorber - the black body, is also the best radiation emitter.Turning on the lightSo a light bulb in the box will also give off “blackbody radiation”. Under equilibrium conditions, the dominant frequency of this radiation depends only on the temperature. The radiation curves were shown to be very similar to Maxwell's velocity distributions of heated gas molecules in a sealed container.Measuring the Frequency as a function of temperatureNote that it doesn’t go to zero hereSeveral FrequenciesNote that the wavelength of the maximum goes decreases as T increasesIT NEVER GOES TO ZERO, NOT FOR ANY TEMPERATUREExplaining ItIn 1879, Joseph Stefan found that power emitted was proportional to T4 (Stefan-Boltzman law)P=T4Wien’s displacement law for the peak value was formulated in 1894pT=constant Both of these are not derivable from 1st principles but only phenomenological descriptionsSimilar to W=mg describes weight on Earth but not gravitationThe “Ultraviolet Catastrophe”Lord Rayleigh and Sir Jeans (1900) calculated the energy distribution using the same theoretical assumptions as Maxwell had done with his kinetic theory of gasses. They applied the statistical physics method to waves by analogy with Maxwell's gas particles using the equipartition of energy, i.e. they assumed that the total energy of radiation is distributed equally among all possible vibration frequencies. In other words, energy is a continuous distribution over all valuesRayleigh-Jeans Law48),(kTTI Blows up at ultraviolet wavelengthsPlanck’s IdeaPlanck explained this by assuming that atoms are small oscillators He used two postulates1. Energy (either emitted or absorbed)  frequencyE  f or using a constant, h, E=hf2. No arbitrary energies … discrete energies only. E= n*h*f where n= 0, 1, 2, .. No ½ values!Walking the Planck…18),(5kThcehcTI•At T=0 K, the oscillators still oscillate (Note I ≠ 0, zero point energy•At high T, Law Jeans-Rayleigh iswhich 88),(1...1818),(4555kTkThchcTIkThchcehcTIkThcPhotoElectric Effect– Einstein’s Only Nobel PrizeIn the 1900s, scientists noted that if a beam of light is shown on the anode, a current is producedClassically, we expect that if we increase the intensity of the light, we will increase the intensity of the currentHowever, the observed phenomenon was that the current flow was basically constant with light strength, yet varied strong with the wavelength of light such that there was a sharp cutoff and no current flow for long wavelengths no matter the intensity!Einstein takes the next step…Based on Planck’s successful theory, he argues that energy changes between oscillators asE=hfFirst, Einstein assumed that some work (or