Chapter 1 The Wave Function

Chapter 1 The Wave Function - Chapter 1 The Wave Function...

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Chapter 1 The Wave Function Section 1.1 Wave-Particle duality Section 1.2 Schrödinger’s equation Section 1.3 Statistical interpretation Section 1.4 Position and Momentum Section 1.5 The uncertainty principle 2009/9/14
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Section 1.1 Wave-Particle duality
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Section 1.1 Wave-Particle duality 19 世纪末: 子性 质是由粒子 粒子性:物质是由粒子(原子,电子,。。。)组成, 它的运动由牛顿定律决定的; 波动性:光是一种波,具有干涉、衍射特性。 Maxwell’s equations of electromagnetic fields; Hertz experiments of light Thomas Young's sketch of two-slit pg as electromagnetic fields diffraction of waves , 1803.
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Section 1.1 Wave-Particle duality 光也是一种粒子 : 1905 Einstein’s light quantum – photon 光子概念的提出 923 ompton’s scattering experiment 也是一种粒子 1923 Compton s scattering experiment 确立 光也是 种粒子 子也是一种波 电子也是一种波 : 1913- Bohr’s quantum theory :对应原理 Sommerfeld 量子化条件 , 1,2,3, pdq nh n == " v
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Section 1.1 Wave-Particle duality Louis de Broglie 892 987) (1892-1987) Nobel Prize in Physics (1929) Simulated photograph of the first Solvay conference in 1911 at the Hotel Metropole. Seated (L-R): W. Nernst, M. Brillouin, E. Solvay, H. Lorentz, E. Warburg, J. Perrin, W. Wien, M. Curie, and H. Poincaré. Standing (L-R): R. Goldschmidt, M. Planck, H. Rubens, A. Sommerfeld, F. Lindemann, M. de Broglie , M. Knudsen, F. Hasenöhrl, G. Hostelet, E. Herzen, J.H. Jeans, E. Rutherford, H. Kamerlingh Onnes, A. Einstein and P. Langevin.
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Section 1.1 Wave-Particle duality 1. Einstein 的光量子公式 中将 粒子的量 E 和波的量 结合在一起,这 无法理解的 Eh ν = 是无法理解的; 2. Bohr 原子理论中的轨道(量子化条件) 是强加的;整数或周期性通常意味着波 的特性。 解决这一矛盾冲突的唯一办法就是 电子等微粒的运动也伴随一种波 Louis de Broglie 892 987) (de Broglie (matter) wave) (1892-1987) Nobel Prize in Physics (1929) 这一想法是受到 Brillouin 1919-1922 发表的一系列关于 Bohr 原子的论文启发。
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Section 1.1 Wave-Particle duality 微粒与对应的波如何联系? 光子: Eh ν = Themomentum of a photon: p =E/c The wavelength / c λ = 对其他的微粒? 虑一个运动速度为 粒子 考虑 个运动速度为 v 的粒子: / vc β≡ (1) 在粒子运动的参照系,粒子静止不动,波乃 在空间任何一处均有 驻波,即在空间任何一处均有 ( ) 00 0 sin 2 t π ντ 0 : τ 常数
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Section 1.1 Wave-Particle duality h 2 00 Eh mc ν == ) 实验室参照系 据狭义相对论 (2) 在实验室参照系,根据狭义相对论,有 / tx c β 0 2 1 t = 2 0 0 2 2 sin 1 1 x t c πν τβ ⎛⎞ −− ⎢⎥ ⎜⎟ ⎝⎠ sin 2 x t τ λ ⎡⎤ =− 2 1 h v = ⎣⎦ 波长: 2 1 c = 0 /1 mv 0 νβ h p λ=
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Section 1.1 Wave-Particle duality De Broglie 的想法可以很自然地与 Bohr 的角动量量子化条件相联系: 在氢原子中电子处在一些稳定的轨道上,若电子也是波,那么,稳定的 条件就是形成驻波: 稳定条件:
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Section 1.1
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This note was uploaded on 09/17/2011 for the course PHYS 130 taught by Professor Wu during the Fall '10 term at Fudan University.