38. Photons and Matter Waves

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38. Potons and Matter Waves Termal Radiation and Black-Body Radiation Color of a Tungsten filament as temperature increases Black Red Yellow Wite T Termal radiation : Te

1 38. Potons and Matter Waves Termal Radiation and Black-Body Radiation Color of a Tungsten filament as temperature increases Black Red Yellow Wite T Termal radiation : Te radiation depends on te temperature and properties of objects Black-body Radiation All te ligt is absorbed. But te radiation depends on te temperature of te inside wall.

2 λmat m K Wien s Displacement law Classic Point of View Te termal radiation was considered to be simply due to accelerated carged particles near te surface. Not rigt! Classical teory Intensity Eperimental Ultraviolet catastrope!! Wavelengt

3 38-. Plank s Teory, te Poton, te Quantum of Ligt Plank --- Eplain te black-body radiation wit two assumptions related to te oscillating carges. 1. Te radiation energy is Quantized. E n nf f c / λ. Te rasonators emit energy, te so-called poton. E f poton energy : Elementary quantity J s ev s Plank succeeded in reproducing te black-body radiation curve. But no body including Plank imself did not accept te quantum concept. -- Considered te assumptions unrealistic.

4 38-3. Te Potoelectric Effect potoelectric effect Potoelectrons, Potoelectric current First Potoelectric Eperiment Te first discovery by Herz in V stop V stop : Stopping potential (independent of te radiation intensity Electrons aving a kinetic energy K K ma ev stop

5 Caracteristics in te potoelectric effect i Cutoff frequency, f 0 f < No potoelectrons f 0 ii K ma is independent of te ligt intensity. iii K f ma iv Potoelectric effect occurs instantaneously ( ~ sec. Cutoff wavelengt c λ0 f 0

6 Einstein (1905 Etend te quantum concept of Plank s Energy of te electromagnetic waves Potons Eac poton can give its energy to a single electron. K ma f Φ Work function V stop e e f Φ e V s f 0 Φ ( V s ( C J s Minimum energy bound in te metal (3 ~ 6 ev i Φ f 0 Cutoff frequency ii K ma f Φ iii Kma f iv Te particle teory of ligt Cutoff wave lengt λ 0 c f 0 c Φ / c Φ

7 38-4. Potons ave Momentum Einstein E f Poton Energy p f / c E / c / λ Poton Momentum H. Compton and P. Debye in 193 carried an eperiment to prove Einstein s point-like particle concept. E f, p E c λ 71.1 pm Te potoelectric effect (-ray scattering: Te total momentum of te poton-electron pair must be conserved. Doppler sift of scattered ligt varies wit te scattered angle φ.

8 Collision - Energy conservation f f + K K mc ( γ 1 f f + mc ( γ 1 1 γ 1 ( v / c + mc( γ 1 λ λ - Momentum conservation cosφ + γmvcosθ λ λ 0 sinφ γmvsinθ λ ( ais ( y ais λ λ Δλ mc ( 1 cosφ (Compton sift λ c mec nm (Compton wavelengt

9 38-5. Ligt as a Probability Wave Ligt as a dual nature, Wave & Poton. Ligt can be a wave in classical pysics but be potons in quantum mecanics. Low frequency : Long wavelengt More wave like Hig frequency : Sort wavelengt More particle like Young s Double slit Eperiment : te evidence for te wave nature of ligt but can be understood as a relative probability for a detection of a single poton.

10 38-6. Electrons and Matter Waves Particle also as a dual nature!! In 194, Louis Victor de Broglie postulated an electron also as a dual nature. Peraps all forms of matter ave wave as well as particle properties. Poton: E f E p λ c λ p Te wavelengt of poton can be defined by te momentum. Electron: p mv de Broglie wave λ p mv : de Broglie wavelegnt frequency of matter f E

11 Te Double-Slit Eperiment Dsinθ λ p λ Minimum λ sin θ θ D Dp Te number of electrons detected at a certain spot is proportional to te intensity of two interfering matter waves.

12 How do we understand te wave-caracter of electrons? Poton EM Wave E r, B r I E Interference effects : Wave function * I 1 + I cosφ Wic slit does te electron pass troug? Slit 1 or Slit

13 De Broglie (193-4: All matters ave a dual nature. Ten an electron must eibit diffraction and interference effects. Davisson-Germer Eperiment (197: Measure te wavelengt of electrons. Crystalized NiO target Diffraction patterns due to electron beam. Etended work on many single-crystalline targets Conclude p λ G. P. Tomson (198 Electron diffraction pattern from electrons passing troug a gold foil Helium atom, Hydrogen atom, Neutron also sow te diffraction pattern. Te matter wave is an Universal Nature

14 38-7. Scrödinger Equation Ψ (,y,z,t : Wave function t i e z y t z y ω Ψ,, (,,, ( ω (πf: angular frequency of matter wave : probability density, and not, as pysical meaning. Scrödinger equation (1-dim: [ ] 0 ( 8 + π U E m d d U (: Potential energy ( π π m p m d d mv m d d 0 + π p d d 0 + k d d Scrödinger equation (free particle λ π λ /, / k p General solution ( (, ( and, ( t k i t k i ik ik Be Ae t Be Ae ω ω + + Ψ +

197 Werner Heisenberg Δ Δp / π It is fundamentally impossible to make simultaneous measurements of a

15 38-8. Heisenberg s Uncertainty Principle Heisenberg Uncertainty Principle A measurement of position is made wit precision Δ, and a measurement of momentum is made wit precision Δp. 197 Werner Heisenberg Δ Δp / π It is fundamentally impossible to make simultaneous measurements of a particle s position and momentum wit infinite accuracy. Similarly ΔE Δt Life-time of a particle p λ Δp λ Position of electron Δ λ Δy Δp y Δp Δ Δz Δp z

16 ( ( + + Δ ( p p p Δ A traveling electron (wave-pocket

17 38-9. Barrier Tunneling T bl e Transmittance T << 1 if were b 8π m( U b E T + R 1 Te Scanning Tunneling Microscope (STM

Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143

Final exam: Tuesday, May 11, 7:30-9:30am, Coates 143 Approximately 7 questions/6 problems Approximately 50% material since last test, 50% everyting covered on Exams I-III About 50% of everyting closely