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12 量子物理

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Sections Photon and Matter Waves Compton Effect Light as a Probability Wave Electrons and Matter Waves Schrodinger ’ s Equation Waves on Strings and Matter Waves Trapping an Electron Three Electron Traps The Hydrogen Atom

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Photon and Matter Waves ( 光子和物質波 ) Light Waves and Photons

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The Photoelectric Effect 光電效應

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First Experiment (adjusting V)– the stopping potential V stop Second Experiment (adjusting f)– the cutoff frequency f 0 The experiment 光電子的最大動能與 光強度無關 低於截止頻率時即使光再 強也不會有光電效應

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The plot of V stop against f

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The Photoelectric Equation Work function

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Compton Effect

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康普吞效應實驗圖表康普吞效應實驗圖表

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康普吞效應圖示

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Energy and momentum conservation

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Frequency shift Compton wavelength

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Light as a Probability Wave The standard version

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The single-photon, double-slit experiment is a phenomenon which is impossible, absolutely impossible to explain in any classical way, and which has in it the heart of quantum mechanics - Richard Feynman The Single-Photon Version First by Taylor in 1909

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The Single-Photon, Wide-Angle Version (1992)

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Light is generated in the source as photons Light is absorbed in the detector as photons Light travels between source and detector as a probability wave The postulate

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Electrons and Matter Waves The de Broglie wave length Experimental verification in 1927 Iodine molecule beam in 1994

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1989 double-slit experiment 7,100,3000, 20,000 and 70,000 electrons

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Experimental Verifications X- ray Electro n beam

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苯環的中子繞射苯環的中子繞射

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Schrodinger ’ s Equation Matter waves and the wave function The probability (per unit time) is Complex conjugate 共軛複數

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The Schrodinger Equation from A Simple Wave Function

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1D Time-independent SE

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3D Time-dependent SE

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Waves on Strings and Matter Waves

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Confinement of a Wave leads to Quantization – discrete states and discrete energies 駐波與量子化 Quantization 駐波：

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Trapping an Electron For a string ：

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Finding the Quantized Energies of an infinitely deep potential energy well

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The ground state and excited states The ground state and excited states The Zero- Point Energy The Zero- Point Energy n can’t be 0 n can’t be 0 The Energy Levels 能階

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The Wave Function and Probability Density For a string

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The Probability Density

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Normalization ( 歸一化 ) Correspondence principle ( 對應原理 ) At large enough quantum numbers, the predictions of quantum mechanics merge smoothly with those of classical physics

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A Finite Well 有限位能井

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The probability densities and energy levels

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Barrier Tunneling 穿隧效應

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STM 掃描式穿隧顯微鏡 Piezoelectricity of quartz

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Three Electron Traps Nanocrystallites 硒化鎘 Nanocrystallites 硒化鎘奈米晶 粒 那種顏色的顆粒比較小

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A Quantum Dot An Artificial Atom The number of electrons can be controlled

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Quantum Corral 量子圍欄

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The Hydrogen Atom The Energies

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氫原子能階與光譜線氫原子能階與光譜線

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Bohr ’ s Theory of the Hydrogen Atom

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The Ground State Wave Function

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Quantum Numbers for the Hydrogen Atom

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The Ground State Dot Plot

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氫原子的量子數

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N=2, l=0, m l =0

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N=2, l=1

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