Chapter 34 Quantum Mechanics Chapter 34 Quantum Mechanics 1. Heisenberg Uncertainty Principle 2. Schrodingers Equation
Chapter 34 Quantum Mechanics Chapter 34 Quantum Mechanics 1. Heisenberg Uncertainty Principle 2. Schrödinger’s Equation
Chapter 34 Quantum Mechanics 8 34-2 The Wave Function and Its Interpretation; The Double-slit Experiment 1. Wave function The important properties of any wave are its wavelength, frequency, and amplitude. a)For eletromagnetic wave 1)Wave length is a measure of the energy. E=hf 2) The amplitude is related to the intensity of the wave
Chapter 34 Quantum Mechanics §34-2 The Wave Function and Its Interpretation; The Double-slit Experiment 1. Wave function The important properties of any wave are its wavelength, frequency, and amplitude. E hf 1) Wave length is a measure of the energy. 2) The amplitude is related to the intensity of the wave. a) For eletromagnetic wave
Chapter 34 Quantum Mechanics a)For de broglie's wave 1)Wave length is related to momentum. 1=h/ 2)What corresponds to the amplitude of a matter wave? In quantum mechanics, this role is played by the wave function, which given the symbol, which is displacement as a function of time and positio given the symbol.It represents th
Chapter 34 Quantum Mechanics h / p 1) Wave length is related to momentum. 2) What corresponds to the amplitude of a matter wave? a) For De Broglie’s wave In quantum mechanics, this role is played by the wave function, which given the symbol, which is g i v e n t h e s y m b o l . It r e p r e s e n ts t h e displacement as a function of time and position.
Chapter 34 Quantum Mechanics 1)经典的波与波函数 ◆机械波 y(x, t)=Acos 2(vt- E(x, t)= Eo coS 2T(vt 电磁波 xλx H(x, t)=Ho cos 2t(vt-) ◆经典波为实函数 12兀(vt- y(x, t)=rel ae 2)量子力学波函数(复函数) Wave Function: 描述微观粒子运动的波函数(x,y,z,)
Chapter 34 Quantum Mechanics 1）经典的波与波函数 ( , ) cos 2π ( ) 0 x E x t E t ( , ) cos 2π ( ) 0 x H x t H t 电磁波 ( , ) cos 2π ( ) x 机械波 y x t A t ( , ) Re[ e ] i 2 π ( ) x t y x t A 经典波为实函数 2）量子力学波函数（复函数） 描述微观粒子运动的波函数 Ψ(x, y,z,t) Wave Function:
Chapter 34 Quantum Mechanics The wave function can be written in two forms The time-dependent version; Y(,v,z, t)=y(x, v, z)e o O=2丌∫— angular frequency of matter wave p is complex in the math sense, i2=-1 and the time-independent version y(x, y, 3) -involves a wave function with only spatial dependence(steady state situations). Two questions arise:
Chapter 34 Quantum Mechanics i t x y z t x y z e ( , , , ) ( , , ) 2 f — angular frequency of matter wave The wave function can be written in two forms: The time-dependent version; and the time-independent version: (x, y,z) — involves a wave function with only spatial dependence (steady state situations). is complex in the math sense, 1 2 i Two questions arise:
Chapter 34 Quantum Mechanics 2. Statistical Meaning of De Broglie's Wave Particle: Energy 8; Momentum p; Quantities N Wave: wavelength n Frequency f; Amplitude Eo Their relation: The numbers of particles Noc I oc Eof The intensity of De broglie's wave somewhere is proportional to the square of the electric field strength. 在某处德布罗意波的强度与粒子在该处邻近出现的概 率成正比
Chapter 34 Quantum Mechanics 2. Statistical Meaning of De Broglie’s Wave: Particle: Energy ; Momentum p; Quantities N Wave: wavelength ; Frequency f ; Amplitude E0 The numbers of particles N I E0 2 The intensity of De Broglie’s wave somewhere is proportional to the square of the electric field strength. Their Relation: 在某处德布罗意波的强度与粒子在该处邻近出现的概 率成正比
Chapter 34 Quantum Mechanics 3. Double- slit experiment电子双缝的衍射实验 减弱入射电子束的强度,让一个一个电子依次通过双 缝,则随着电子树的积累,衍射图样依次如图 7个电子 100个电子 底片上出现一个个的点子→电子具有粒子性
Chapter 34 Quantum Mechanics 3. Double-slit experiment 电子双缝的衍射实验 减弱入射电子束的强度，让一个一个电子依次通过双 缝，则随着电子树的积累，衍射图样依次如图。 7个电子 100个电子 底片上出现一个个的点子电子具有粒子性
Chapter 34 Quantum Mechanics 3000 20000 70000 随着电子增多,逐渐形成衍射图样。 来源于“一个电子”所具有的波动性,而不是电子间 相互作用的结果
Chapter 34 Quantum Mechanics 70000 3000 20000 随着电子增多，逐渐形成衍射图样。 来源于“一个电子”所具有的波动性，而不是电子间 相互作用的结果
Chapter 34 Quantum Mechanics 单个粒子在哪一处出现是偶然事件; 大量粒子的分布有确定的统计规律。 出现概率小 出现概率大 电子数N=70000
Chapter 34 Quantum Mechanics 电子数 N=71320000 单个粒子在哪一处出现是偶然事件； 大量粒子的分布有确定的统计规律。 出现概率小 出现概率大 电 子 双 缝 干 涉 图 样
Chapter 34 Quantum Mechanics 玻恩( M. Born):尽管单个电子的去向是概率性 的,但其概率在一定条件下(如双缝),还是有确定 的规律的。 德布罗意波并不是经典的波那样是代表实在物理 量的波动。在双缝实验中。不管入射波强度如何小, 经典的波在缝后的屏幕上都“应该”显示出强弱连续 分布的衍射条纹,只是亮度微弱而已。但图中明确地 显示物质波的主体仍是粒子,而且该种粒子的运动并 不具有经典的振动形式
Chapter 34 Quantum Mechanics 玻恩（M.Born）：尽管单个电子的去向是概率性 的，但其概率在一定条件下（如双缝），还是有确定 的规律的。 德布罗意波并不是经典的波那样是代表实在物理 量的波动。在双缝实验中。不管入射波强度如何小， 经典的波在缝后的屏幕上都“应该”显示出强弱连续 分布的衍射条纹，只是亮度微弱而已。但图中明确地 显示物质波的主体仍是粒子，而且该种粒子的运动并 不具有经典的振动形式