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## Modern Physics: Quantum Mechanics

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**Modern Physics: Quantum Mechanics**• Physics changed drastically in the early 1900’s • New discoveries — Relativity and Quantum Mechanics • Relativity • Changed the way we think about space and time • Quantum mechanics • Changed our conceptions of matter. Phy107 Fall 2006**Course essay**• Friday, Nov 3: Due in class — essay topic(review article, operating experiment, noble prize) short description - one paragraphhttp://www.hep.wisc.edu/~herndon/107-0609/essay.htm • Friday, Nov 17Due in class — essay outline main article reference • Friday, Dec. 8Due in class — final typed essay. Phy107 Fall 2006**Quantum mechanics**• The quantum mechanical world is VERY different! • Energy not continuous, but can take on only particular discrete values. • Light has particle-like properties, so that light can bounce off objects just like balls. • Particles also have wave-like properties, so that two particles can interfere just like light does. • Physics is not deterministic, but events occur with a probability determined by quantum mechanics. Phy107 Fall 2006**Origins of quantum mechanics**• Late 1800s: • Maxwell’s equations describe propagation of EM waves in detail. • Electricity and magnetism progress from basic science to technological applications. Photoelectric effect, Blackbody radiation spectrum, • Early 1900s: • Further Investigations into light, and interaction of light with matter, hint at some scary ideas • Simultaneous with relativity say that energy is quantized in discrete units. Phy107 Fall 2006**Energy quantization in a pendulum**Swinging pendulum. Larger amplitude, larger energy Small energy Large energy Quantum mechanics: Not every swing amplitude is possibleenergy cannot change by arbitrarily small steps Phy107 Fall 2006**Energy quantization**• Energy can have only certain discrete values Energy states are separated by E = hf.f = frequencyh = Planck’s constant= 6.626 x 10-34 J-s E= hf=3.3x10-34 J for pendulum = spacing between energy levels Suppose the pendulum has Period = 2 secFreq = 0.5 cycles/sec • E=mgd=(1 kg)(9.8 m/s2)(0.2 m) ~ 2 Joules • Emin=hf=3.3x10-34 J << 2 J • Quantization not noticeable d Phy107 Fall 2006**Energy of light**• Quantization also applies to other physical systems • In the classical picture of light (EM wave), we change the brightness by changing the power (energy/sec). • This is the amplitude of the electric and magnetic fields. • Classically, these can be changed by arbitrarily small amounts Phy107 Fall 2006**E=4hf**E=3hf E=2hf E=hf Quantization of light • Quantum mechanically, brightness can only be changed in steps, with energy differences of hf. • Possible energies for green light (=500 nm) • One quantum of energy:one photon • Two quanta of energytwo photons • etc • Think about light as a particle rather than wave. Phy107 Fall 2006**The particle perspective**• Light comes in particles called photons. • Energy of one photon is E=hf f = frequency of light • Photon is a particle, but moves at speed of light! • This is possible because it has zero mass. • Zero mass, but it does have momentum: • Photon momentum p=E/c Phy107 Fall 2006**One quantum of green light**• One quantum of energy for 500 nm light Quite a small energy! Quantum mechanics uses new ‘convenience unit’ for energy: 1 electron-volt = 1 eV = |charge on electron|x (1 volt) = (1.602x10-19 C)x(1 volt) 1 eV = 1.602x10-19 J In these units, E(1 photon green) = (4x10-19J)x(1 eV / 1.602x10-19 J) = 2.5 eV Phy107 Fall 2006**Simple relations**• Translation between wavelength and energyhas simple form in electron-volts and nano-meters Green light example: Phy107 Fall 2006**Photon properties of light**• Photon of frequency f has energy hf • Red light made of ONLY red photons • The intensity of the beam can be increased by increasing the number of photons/second. • Photons/second = energy/second = power Phy107 Fall 2006**Shorter path**Longer path But light is a wave! • Light has wavelength, frequency, speed • Related by f = speed. • Light shows interference phenomena • Constructive and destructive interference L Light beam Recording plate Foil with two narrow slits Phy107 Fall 2006**Wave behavior of light: interference**Phy107 Fall 2006**Particle behavior of light: photoelectric effect**• A metal is a bucket holding electrons • Electrons need some energy in order to jump out of the bucket. Light can supply this energy. Energy transferred from the light to the electrons. Electron uses some of the energy to break out of bucket. Remainder appears as energy of motion (kinetic energy). A metal is a bucket of electrons. Phy107 Fall 2006**Unusual experimental results**• Not all kinds of light work • Red light does not eject electrons More red light doesn’t either No matter how intense the red light, no electrons ever leave the metal Until the light wavelength passes a certain threshold, no electrons are ejected. Phy107 Fall 2006**Wavelength dependence**Short wavelength: electrons ejected Long wavelength: NO electrons ejected Threshold depends on material Lo-energy photons Hi-energy photons Phy107 Fall 2006**Einstein’s explanation**• Einstein said that light is made up of photons, individual ‘particles’, each with energy hf. • One photon collides with one electron - knocks it out of metal. • If photon doesn’t have enough energy, cannot knock electron out. • Intensity ( = # photons / sec) doesn’t change this. Minimum frequency (maximum wavelength) required to eject electron Phy107 Fall 2006**Summary of Photoelectric effect**• Explained by quantized light. • Red light is low frequency, low energy. • (Ultra)violet is high frequency, high energy. • Red light will not eject electron from metal,no matter how intense. • Single photon energy hf is too low. • Need ultraviolet light Phy107 Fall 2006**Photon properties of light**• Photon of frequency f has energy hf • Red light made of ONLY red photons • The intensity of the beam can be increased by increasing the number of photons/second. • Photons/second = energy/second = power Interaction with matter • Photons interact with matter one at a time. • Energy transferred from photon to matter. • Maximum energy absorbed is photon energy. Phy107 Fall 2006**Photon Energy**A red and green laser are produce light at a power level of 2.5mW. Which one produces more photons/second? • Red • Green • Same Red light has less energy per photon so needs more photons! Phy107 Fall 2006**Why is all this so important?**• Makes behavior of light wave quite puzzling. • Said that one photon interacts with one electron, electron ejected. • If this wavefront represents one photon, where is the photon? • Which electron does it interact with? • How does it decide? Light hitting metal Phy107 Fall 2006**Neither wave nor particle**• Light in some cases shows properties typical of waves • In other cases shows properties we associate with particles. • Conclusion: • Light is not a wave, or a particle, but something we haven’t thought about before. • Reminds us in some ways of waves. • In some ways of particles. Phy107 Fall 2006**Only one photon present here**Photon interference? Do an interference experiment again. But turn down the intensity until only ONE photon at a time is between slits and screen ? Is there still interference? Phy107 Fall 2006**100 sec exposure**1 sec exposure Single-photon interference 1/30 secexposure Phy107 Fall 2006**P.A.M. Dirac (early 20th century):**• “… each photon interferes with itself.Interference between different photons never occurs.” We now can have ‘coherent’ photons in a laser,(Light Amplification by Stimulated Emission of Radiation) invented 40 years ago. These photons can in fact interfere. Phy107 Fall 2006**Probabilities**• We detect absorption of a photon at camera. • Cannot predict where on camera photon will arrive. • Position of an individual photon hits is determined probabilistically. • Photon has a probability amplitude through space. Square of this quantity gives probability that photon will hit particular position on detector. • The photon is a probability wave! The wave describes what the particle does. Phy107 Fall 2006**Before collision**After collision Compton scattering • Photon loses energy, transfers it to electron • Photon loses momentum transfers it to electron • Total energy and momentum conserved Photon energy E=hfPhoton mass = 0Photon momentum p=E/c Phy107 Fall 2006**Compton scattering**• Photons can transfer energy to beam of electrons. • Determined by conservation of momentum, energy. • Compton awarded 1927 Nobel prize for showing that this occurs just as two balls colliding. Arthur Compton, Jan 13, 1936 Phy107 Fall 2006**The Black Body spectrum**• Light radiated by an object characteristic of its temperature, not its surface color. • Spectrum of radiation changes with temperature Phy107 Fall 2006**Spectrum changes with temperature**• The wavelength of the peak of the blackbody distribution was found to follow • Peak wavelength shifts with temperature • max is the wavelength at the curve’s peak • T is the absolute temperature of the object emitting the radiation Phy107 Fall 2006**The ‘color’ of a black body**• Eye interprets colors by mixing cone responses. • Different proportions make object appear different colors. =530 nm =580 nm =440 nm Phy107 Fall 2006**‘Orange’ hot**• Temperature = 4000 K • Combine three cone responsesLong-wavelength cone weighted most heavily Phy107 Fall 2006**‘White’ hot**• Temperature = 5000 K • Spectrum has shifted so that colors are more equally represented — white hot Phy107 Fall 2006**Representation on color chart**• Apparent color of blackbody at various temperatures. Phy107 Fall 2006**Classical theory**• Classical physics had absolutely no explanation for this. • Only explanation they had gave ridiculous answer. • Amount of light emitted became infinite at short wavelength • Ultraviolet catastrophe Phy107 Fall 2006**Explanation by quantum mechanics**• Blackbody radiation spectrum could only be explained by quantum mechanics. • Radiation made up of individual photons, each with energy (Planck’s const)x(frequency). • Very short wavelengths have very high energy photons. • Minimum energy is 1 photon. • For shorter wavelength’s even 1 photon is too much energy, so shortest wavelengths have very little intensity. Phy107 Fall 2006