Chapter 34 Quantum Mechanics 4. Probability Density I y2, which we call the probability density The probability (per unit time)of detecting a particle in a small volume centered on a given point in a matter wave is proportional to the value of y2 at that point 电子的状态用波函数y描述,在P处附近 d内发现粒子的概率是波函数的模方 玻恩1926年给出的y的统计解释 德布罗意波并不像经典波那样代表实在的物理量的 波动,而是刻画粒子在空间的概率分布的概率波
Chapter 34 Quantum Mechanics | |2 , which we call the probability density 德布罗意波并不像经典波那样代表实在的物理量的 波动，而是刻画粒子在空间的概率分布的概率波。 The probability (per unit time) of detecting a particle in a small volume centered on a given point in a matter wave is proportional to the value of | |2 at that point . r 电子的状态用波函数 描述，在 处附近 dV内发现粒子的概率是波函数的模方。 ——玻恩1926年给出的 的统计解释 4. Probability Density
Chapter 34 Quantum Mechanics 波函数的统计意义 概率密度表示在某处单位体积内粒子出现的概率 W"正实数 某一时刻出现在某点附近在体积元d中的粒子 的概率为 y*dv=rdv 某一时刻在整个空间内发现粒子的概率为 归一化条件∫vd
Chapter 34 Quantum Mechanics 某一时刻出现在某点附近在体积元 中的粒子 的概率为 dV Ψ dV Ψ dV 2 * Ψ d 1 2 归一化条件 Ψ V 某一时刻在整个空间内发现粒子的概率为 波函数的统计意义 2 * Ψ 概率密度 表示在某处单位体积内粒子出现的概率. 正实数
Chapter 34 Quantum Mechanics §34-3 Heisenbergs Uncertainty principle(不确定度) Heisenbergs uncertainty principle, proposed in 1927 by german physicist Werner Heisenberg. It states that measured values cannot be assigned to the position r and the momentum p of a particle simultaneously with unlimited precision For the components of r and p, heisenbergs principle gives the following limits in terms 0fh=h/2兀, AxAp≥h,AAP≥h,△△P2≥h Heisenberg uncertainty (indeterminancy) principle
Chapter 34 Quantum Mechanics §34-3 Heisenberg’s Uncertainty Principle(不确定度) Heisenberg's uncertainty principle, proposed in 1927 by German physicist Werner Heisenberg. It states that measured values cannot be assigned to the position and the momentum of a particle simultaneously with unlimited precision. r p For the components of and , Heisenberg's principle gives the following limits in terms of =h/2 . r p x y z x p , y p , z p Heisenberg uncertainty (indeterminancy) principle
Chapter 34 Quantum Mechanics ◆海森伯于1927年提出不确定原理 对于微观粒子不能同时用确定的位置和确定的 动量来描述 △x△Px≥h 不确定关系 y△p h △z△P≥h Where Ap, Ap, and Ap, are the uncertainty of the momentum in the x, y and z directions. h6.626×1034J.s h =1055×1034J·s 2 2丌
Chapter 34 Quantum Mechanics 海森伯于 1927 年提出不确定原理 对于微观粒子不能同时用确定的位置和确定的 动量来描述 . yp y h xp x h z p h z 不确定关系 Where are the uncertainty of the momentum in the x, y and z directions. x y z p , p and p 1.055 10 J s 2 6.626 10 J s 2 34 34 h
Chapter 34 Quantum Mechanics Even with the best measuring instruments that technology could ever provide, each product of a position uncertainty and a momentum uncertainty in above equations will be greater than h; it can never be less. 当粒子位置的不确定度Δx小时,动量的不确定度Δp就大, 反之亦然.即微观粒子不可能同时具有确定的位置和动量 For example,if△p→>0;△x→>o For ideal homochromatic plane-wave理想的单色 平面波,△p=0→△→>0 h>0, Quantum physics- Classical physics
Chapter 34 Quantum Mechanics For ideal homochromatic plane-wave 理想的单色 平面波, p 0; x p 0 x For example, if Even with the best measuring instruments that technology could ever provide, each product of a p o siti o n u n c e r t a i n t y a n d a m o m e n t u m uncertainty in above equations will be greater than ; it can never be less. 当粒子位置的不确定度x小时,动量的不确定度p就大, 反之亦然.即微观粒子不可能同时具有确定的位置和动量. h 0, Quantum physics Classical physics