量子力学英文名词 ppt课件
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量子力学英文课件格里菲斯Charter10
In molecular physics, this technique is known as the Born-Oppenheimer （玻恩-奥本海默）approximation.
In quantum mechanics, the essential content of the adiabatic approximation can be cast in the form of a theorem.
Here we assume that the spectrum is discrete and nondegenerate throughout the transition from Hi to Hf , so there is no ambiguity（歧义） about the
ordering of the states; these conditions can be relaxed, given a suitable procedure for “tracking” （跟踪）the eigenfunctions, but we’re not going to pursue that
A case in point is our discussion of the hydrogen molecule ion.
We began by assuming that the nuclei were at rest, a fixed distance R apart, and we solved for the motion of the electron.
and they are complete, so the general solution to the time-dependent Schrödinger equation
量子力学英文课件格里菲斯Chapter6
Writing n and En as power series in , we have
Here : En1 is the first-order correction to the nth eigenvalue, n1 is the first-order correction to the nth eigenfunction; En2 and n2 are the second-order corrections, and so on.
To first order (1),
To second order (2),
and so on. We’re done with , now — it was just a device to keep track of the different orders — so crank it up to 1.
The right side is a known function, so this amounts to an inhomogeneous differential equation for n1. Now, the unperturbed wave functions constitute a complete set, so n1 (like any other function) can be expressed as a linear combination of them:
but unless we are very lucky, we’re unlikely to be able to solve the Schrö dinger equation exactly, for this more complicated potential. Perturbation theory is a systematic procedure for obtaining approximate solutions to the perturbed problem by building on the known exact solutions to the unperturbed case.
量子力学英文课件格里菲斯Charter8
It is particularly useful in calculating bound-state energies and tunneling rates through potential barriers.
The essential idea is as follows: Imagine a particle of energy E moving through a region where the potential V(x) is constant.
Suppose we have an infinite square well with a bumpy bottom (Figure 8.2):
Inside the well [assuming E > V(x) throughout] we have or, more conveniently, where
rather slowly in comparison to , so that over a region
containing many full wavelengths the potential is essentially constant.
Then it is reasonable to suppose that remains
F is the transmitted amplitude, and the tunneling probability is
In the tunneling region ( 0 x a ), the WKB approximation gives
But if the barrier is very high and/or very wide, then the coefficient of the exponentially increasing term (C) must be small, and the wave function looks something like Figure 8.4.
The essential idea is as follows: Imagine a particle of energy E moving through a region where the potential V(x) is constant.
Suppose we have an infinite square well with a bumpy bottom (Figure 8.2):
Inside the well [assuming E > V(x) throughout] we have or, more conveniently, where
rather slowly in comparison to , so that over a region
containing many full wavelengths the potential is essentially constant.
Then it is reasonable to suppose that remains
F is the transmitted amplitude, and the tunneling probability is
In the tunneling region ( 0 x a ), the WKB approximation gives
But if the barrier is very high and/or very wide, then the coefficient of the exponentially increasing term (C) must be small, and the wave function looks something like Figure 8.4.
量子力学英文格里菲斯Chapter2PPT课件
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Once we have found the separable solutions, then, we can immediately construct a much more general solution, of the form
It so happens that every solution to the (time dependent) Schrödinger equation can be written in this form — it is simply a matter of finding the right constants (c1, c2, c3, c4, …）so as to fit the initial conditions for the problem at hand.
4
Now the left side is a function of t alone, and the right side is a function of x alone.
5
The only way this can be possibly be true is if both sides are in fact constant, we shall call the separation constant E. Then
But before we get to that we would like to consider further the question:
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What’s so great about separable solution ?
可分离的解（即 (x,t)=(x) f(t) ）为何如此重要？
After all, most solutions to the (time-dependent)
Once we have found the separable solutions, then, we can immediately construct a much more general solution, of the form
It so happens that every solution to the (time dependent) Schrödinger equation can be written in this form — it is simply a matter of finding the right constants (c1, c2, c3, c4, …）so as to fit the initial conditions for the problem at hand.
4
Now the left side is a function of t alone, and the right side is a function of x alone.
5
The only way this can be possibly be true is if both sides are in fact constant, we shall call the separation constant E. Then
But before we get to that we would like to consider further the question:
7
What’s so great about separable solution ?
可分离的解（即 (x,t)=(x) f(t) ）为何如此重要？
After all, most solutions to the (time-dependent)
量子力学英文课件格里菲斯Charter9
If we want to allow for transitions between one energy level and another, we must introduce a time-dependent potential (quantum dynamics).
There are precious few exactly solvable problems in quantum dynamics.
where
We’ll assume that Eb > Ea , so 0 0. 0 —— transition frequency
So far, everything is exact: We have made no assumption about the size of the perturbation.
The only difference is that ca and cb of Eq.[9.4] are now functions of t :
Now, the whole problem is to determine ca(t) and cb(t) as functions of time.
dcb/dt, from Eq.[9.8] we have :
and hence
Eqs.[9.10] and [9.11] determine ca(t) and cb(t); taken together, they are completely equivalent to the (time-dependent) Schrodinger equation, for a twolevel system.
However, if the time-dependent portion of the Hamiltonian is small compared to the time independent part. it can be treated as a perturbation.
量子力学英文名词
物理学名词中英文对照
斯特藩-玻耳 Stefan-Boltzmann law 兹曼定律 斯特藩常量 Stefan constant 维恩位移定律 Wien displacement law 瑞利-金斯公式 Rayleigh-Jens formula 普朗克辐射公式 Planck radiation formula 普朗克常量 Planck constant
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物理学
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能带 基态 激发态 弗兰克赫兹实验 德布罗意波 德布罗意波长
energy band ground state excitation state Franck-Hertz experiment De Broglie wave De Broglie wavelength
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物理学
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物理学
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普丰得系 玻尔量子 化条件 玻尔氢原子 玻尔频率条件 玻尔半径 能级
Pfund series Bohr quantization condition Bohr hydrogen atom Bohr frequency condition Bohr radius energy level
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物理学
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物理学
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康普顿效应 康普顿散射 康普顿波长 反冲电子 莱曼系 帕邢系 布拉开系
Compton effect Compton scattering Compton wavelength recoil electron Lyman series Paschen series Brackett series
Chapter 2 The Schrodinger Equation 量子力学英文教案课件
The principle of the superposition state back
（1） The principle of the superposition state （2） The wave function in momentum space
ω( r, t )= {dW(r, t )/ dτ}= C |Ψ (r,t)|2
W(t)=∫V dW =∫Vω( r, t )dτ= C∫V|Ψ (r,t)|2 dτ
University of Electronic Science and Technology of China
2005-3-1
Prof. Zhang Xiaoxia©
back
Chapter 2 The Schrodinger Equation
The Interpretation of the Wave Function The principle of the superposition state Average value of dynamics quantity and Differential Operators Schrodinger Equation Time-independent Schrodinger Equation The Heisenberg Uncertainty Relation
p (r ,t)[2 1]3/2e i[p •r E]t p (r )e iEt
where
1
p(r)[2]3/2
i[p•r]
e
University of Electronic Science and Technology of China
2005-3-1
Prof. Zhang Xiaoxia©
量子力学入门 英语
Einstein
In 1913，Bohr proposed that electrons travel only in certain orbits and that any atom could exist only in a discrete set of stable states，and developed a new theory of the atom. 1913年，波尔提出了电子是按固 定轨道运行和电子只能处于一些 离散的稳定状态的假设。在此基 础上，他推动了新的原子理论的 发展。
1900年，普朗克提出能量的发射和吸 收是按“一份一份”进行的假说 ，这 个假说成功的解释了黑体辐射模型。
Planck
• in 1905 ，Einstein used Planck’s quantum hypothesis realistically to explain the photoelectric effect. • 1905年，爱因斯坦用普朗克 的量子假设成功地解释了光 电效应。
Can a particle escape from the black hole ? It is still a unsolved mystery . 一个粒子能成黑洞中跑出来吗？这至今是个未解之谜。
Round two : About Velocity 第二回合：关于速度 第二回合：关于速度 According to the relativity theory , nothing can travel faster than light velocity . But quantum entanglement shows us that one particle can affect another with no time , no information. 根据相对论，没有什么东西比光速还快。但量子纠缠态 向我们展示，一个粒子能在瞬间影响其它地方的粒子， 并且不需要传递什么作用力。
In 1913，Bohr proposed that electrons travel only in certain orbits and that any atom could exist only in a discrete set of stable states，and developed a new theory of the atom. 1913年，波尔提出了电子是按固 定轨道运行和电子只能处于一些 离散的稳定状态的假设。在此基 础上，他推动了新的原子理论的 发展。
1900年，普朗克提出能量的发射和吸 收是按“一份一份”进行的假说 ，这 个假说成功的解释了黑体辐射模型。
Planck
• in 1905 ，Einstein used Planck’s quantum hypothesis realistically to explain the photoelectric effect. • 1905年，爱因斯坦用普朗克 的量子假设成功地解释了光 电效应。
Can a particle escape from the black hole ? It is still a unsolved mystery . 一个粒子能成黑洞中跑出来吗？这至今是个未解之谜。
Round two : About Velocity 第二回合：关于速度 第二回合：关于速度 According to the relativity theory , nothing can travel faster than light velocity . But quantum entanglement shows us that one particle can affect another with no time , no information. 根据相对论，没有什么东西比光速还快。但量子纠缠态 向我们展示，一个粒子能在瞬间影响其它地方的粒子， 并且不需要传递什么作用力。
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物理学
第五版
物理学
第五版
康普顿效应 康普顿散射 康普顿波长 反冲电子 莱曼系 帕邢系 布拉开系
物理学名词中英文对照
Compton effect Compton scattering Compton wavelength recoil electron Lyman series Paschen series Brackett series
附录
6
物理学
第五版
物理学
第五版
物理学名词中英文对照
德布罗意公式 物质波 戴维孙-革末实验
不确定关系 波函数
De Broglie formula matter wave Davisson Germer experiment uncertainty relation wave functionBiblioteka 附录7物理学
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势阱
potential well
对应原理 correspondence principle
隧道效应 tunneling effect
能量量子化 energy quantization
主量子数 principal quantum number
角动量量子化 angular quantization
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物理学
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物理学
第五版
普丰得系 玻尔量子 化条件 玻尔氢原子 玻尔频率条件
玻尔半径 能级
物理学名词中英文对照
Pfund series Bohr quantization condition Bohr hydrogen atom Bohr frequency condition Bohr radius energy level
物理学
第五版
物理学
第五版
量子理论 量子力学 量子化 黑体 黑体辐射 黑洞
物理学名词中英文对照
quantum theory quantum mechanics quantization black body black-body radiation black hole
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物理学
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概率密度 概率波 归一化条件 薛定谔方程 定态 定态薛定谔方程
probability density probability wave normalizing condition Schrödinger equation stationary state stationary Schrödinger equation
number
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能量子 光电效应 光电子 光电流 遏止电势差 红限 波粒二象性
energy quantum photoelectric effect photo electron photocurrent cutoff potential difference red-limit wave-particle dualism
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物理学
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物理学
第五版
物理学名词中英文对照
能带 基态 激发态 弗兰克赫兹实验 德布罗意波 德布罗意波长
energy band ground state excitation state Franck-Hertz experiment
De Broglie wave De Broglie wavelength
物理学名词中英文对照
斯特藩-玻耳 Stefan-Boltzmann law 兹曼定律 斯特藩常量 Stefan constant 维恩位移定律 Wien displacement law 瑞利-金斯公式 Rayleigh-Jens formula 普朗克辐射公式 Planck radiation formula 普朗克常量 Planck constant
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物理学
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物理学
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物理学名词中英文对照
角量子数 angle quantum number 空间量子化 space quantization 磁量子数 magnetic quantum number 电子自旋 electron spin 自旋量子数 spin quantum number 自旋磁量子数 spin magnetic quantum