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量子力学英文课件格里菲斯Charter10

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

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Charter9

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.
复旦量子力学讲义qmapter-PPT精品

复旦量子力学讲义qmapter-PPT精品

2020/2/16
§3.4 Dirac equation in the central force field
s(18m h2 2c2 2)(18m p2 2 c2)
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§3.4 Dirac equation in the central force field
Es (18m p22c2) V2pm 2 4Em'2pc224m12c2(rpr)V(rpr)(18m p22c2)s
§3.1 Klein – Gordon equation
➢Non-relativistic limit: K-G eq Sch eq
2020/2/16
§3.1 Klein – Gordon equation
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§3.1 Klein – Gordon equation
2m ihc2['( t'im hc2')'*( t'im hc2')] '*'*
Chapter 3 Relativistic Quantum Mechanics
2020/2/16
2020/2/16
Introduction
➢Non-relativistic quantum mechanics relativistic quantum mechanics
➢Schrödinger equation ➢Klein-Gordon equation S ~ integer ➢Dirac equation S ~ half integer ➢Spin is automatically contained in Dirac
2020/2/16
§3.1 Klein – Gordon equation
量子力学英文课件格里菲斯Charter8

量子力学英文课件格里菲斯Charter8


The second equation [8.7] is easily solved:
where C is a (real) constant.
The first equation [8.6] cannot be solved in general - so here comes the approximation: We assume that the amplitude A varies slowly, so that the A" term is negligible.
In that case we can drop the left side of Eq.[8.6], and we are left with
ቤተ መጻሕፍቲ ባይዱ
and therefore
It follows, then, that
and the general (approximate) solution will be a linear combination of two such terms, one with each sign.
So far, we have assumed that E > V, so that p(x) is real.
But we can easily write down the corresponding result in the nonclassical region (E < V ) – it’s the same as before (Eq.[8.10]), only now p(x) is imaginary:
which are precisely the energy levels of the original infinite square well (Eq.[2.23]). In this case the WKB approximation yields the exact answer.
Chapter 2 The Schrodinger Equation 量子力学英文教案课件

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

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。
量子力学英文课件格里菲斯chapter0

量子力学英文课件格里菲斯chapter0


1925—1927年是物理学急剧变革的年代！
1925年：7月海森伯发表创建量子力学的第一篇论文 9月玻恩、约当认识到需要一种矩阵力学 11月玻恩、约当、海森伯给出矩阵力学 11月狄拉克提出量子代数 1926年：1月薛定谔发表第一篇波动力学论文 7月玻恩发表第一篇量子力学统计解释论文 8月狄拉克提出波函数与粒子统计性质的关系 1927年：3月海森伯测不准关系提出 5月泡利矩阵提出 9月玻尔提出互补原理
Part I Theory
Chap.1 The Wave Function Chap.2 The Time-Independent Schrodinger Equation Chap.3 Formalism Chap.4 Quantum Mechanics in Three Dimensions Chap.5 Identical Particles
(但我们所“做”的和我们所讲的这些故事，就像“舍赫拉查德的传说”一样变化多端， 令人难以置信)
Tales of Scheherazade
Queen Scheherazade (舍赫拉查德 ) tells her stories to King Shahryar (山鲁亚尔 ) !
One Thousand and One Nights
Why should we study the Quantum Mechanics ? What is the Quantum Mechanics ? How to study Quantum Mechanics ?
实验
Comparison of Rayleigh-Jeans law with Wien's law and Planck's law, for a body of 8 mK temperature. /wiki/Rayleigh-Jeans_law
量子力学英文课件格里菲斯Chapter5

量子力学英文课件格里菲斯Chapter5


Moreover, if a system starts out in such a state, it will remain in such a state !
The new law (symmetrization requirement) is that:
for identical particles the wave function is not merely allowed, but required to satisfy Eq.[5.14] , with the plus sign for bosons and the minus sign for fermions.
The statistical interpretation carries over in the obvious way:
Hale Waihona Puke is the probability of finding particle 1 in the volume d3r1 and particle 2 in the volume d3r2 . Evidently must be normalized in such a way that
and E is the total energy of the system.
Suppose particle 1 is in the (one-particle) state a(r), and particle 2 is in the state b(r).
In that case, (r1,r2) is a simple product:
Quantum mechanics neatly accommodates the existence of particles that are indistinguishable in principle : We simply construct a wave function that is noncommittal as to which particle is in which state. There are actually two ways to do it:
量子力学学习课件第三章英文版

量子力学学习课件第三章英文版

(1) hermitian? In this case: As is the usual polar coordinate:
On the interval
(2) The eigenvalue equation, The general solution is By using periodic boundary condition
Therefore, the set of all square-integrable functions, on a specified interval,
constitutes a (much smaller) vector space.
Mathematicians call it L2(a,b), while physicists call it Hilbert space.
the addition and the inner product
The inner product of two vectors, which generalizes the dot product in three dimensions, is defined by
2. Linear transformations
In an N-dimensional space, the vector is represented by a N-number of its components, with respect to a specified orthonormal basis:
We can define operations on vectors:
Some important concepts
On state
we measure an observable Q.
量子力学原理_[英文版](P.A.M.Dirac[著])PPT模板

量子力学原理_[英文版](P.A.M.Dirac[著])PPT模板

§37电子的自 旋
0 2
§35角动量
0 5
§38在有心力 场中的运动
0 3
§36角动量的 性质
0 6
§39氢原子的 能级
第6章初等应用
§40选择定则 §41氢原子的塞曼效应
07
第7章微扰理论
第7章微扰理 论
§42概述
§47反常塞
01
曼 效 应 06
§43微扰引 起的能级 02 变 化
§46与时
02
第2章动力学变量与可观察量

与第
可 观 察 量
章 动 力 学
变
量
2
§7线 性算符
§10可 观察量
§8共 轭关系
§11可观 察量的函
数
§9本征值 与本征矢
量
§12普遍 的物理解
释
第2章动力学变量 与可观察量
§13对易性与相容性
03
第3章表象理论
第3章表象理 论
1 §14基矢量
与散射
§62对光子 的应用
§63光子与 原子间的相
互作用能
§59玻色子 系集
§60玻色子 与振子之间
的联系
§61玻色子 的发射与吸
收
第10章辐射理论
§65费米子系集
11
第11章电子的相对论性理论
第11章电子的相对论性理论
A
§66粒子 的相对论
性处理
B
§67电子 的波方程
C
§68洛伦 兹变换下 的不变性
量子力学原 理:[英文 版 ] ( P. A . M . D i r ac[著])
演讲人 2 0 2 X - 11 - 11
01
第1章叠加原理
第1章叠加 原理

量子力学英文课件格里菲斯Chapter2


Curiously, the boundary condition at x = a does not determine the constant A, but rather the constant k, and hence the possible values of E can be obtained from Eq.[2.17] and [2.22]:
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) Schrö dinger 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.
Equation [2.17] is the (classical) simple harmonic oscillator equation; the general solution is
Typically, these constants are fixed by the boundary conditions of the problem. What are the appropriate boundary conditions for (x)?

量子力学英文课件格里菲斯Chapter3


Technically, a Hilbert space is a complete inner product space, and the collection of square-integrable functions is only one example of a Hilbert space. In quantum mechanics, then,
Outline
In the last two chapters, we have stumbled on a number of interesting properties of simple quantum systems. Some of these are ―accidental‖ features of specific potentials (the even spacing of energy levels for the harmonic oscillator, for example), but others seem to be more general, and it would be nice to prove them once and for all (the uncertainty principle, for instance, and the orthogonality of stationary states).
A set of functions, { fn }, is orthonormal if they are normalized and mutually orthogonal:
Finally, a set of functions is complete if any other function g(x) (in Hilbert space) can be expressed as a linear combination of them:

量子力学英文课件格里菲斯Chapter7


Example 2. Suppose we’re looking for the ground state energy of the delta function potential:
Again, we already know the exact answer (Eq.[2.109]): Eg= m2/2ħ2. (i) As before, we’ll use a gaussian trial wave function with a parameter b (Eq.[7.2]). We’ve already determined the normalization and calculated T; all we need is
Of course, we already know the exact answer, in this case (Eq.[2.49]): Eg = (1/2)ħ; but this makes it a good test of the method. (i) We might pick as our “trial”(尝试) wave function the gaussian,
where A is determined normalization:
On the one hand, according to the theorem:
On the other hand, the Hamiltonian H of the onedimensional infinite square well is
(ii) Evidently
(iii) and we know that this exceeds Eg for all b. Minimizing it,

量子力学英文课件格里菲斯Chapter4


Outside the well the wave function is zero; inside the well the radial equation says
where
Our problem is to solve this equation, subject to the boundary condition : u(a)=0. The case l = 0 is easy:
In other words, exp[im(+2)]=exp[im], or exp(i2m) =1. From this it follows that m must be an integer :
(ii). The equation [4.20]
may not be so familiar. The solution is
批注本地保存成功开通会员云端永久保存去开通
Outline
The generalization to three dimensions is straight forward. Schrödinger’s equation says
where the Hamiltonian operator H is obtained from the classical energy
contains an extra piece, centrifugal term, (ħ2/2m)[l(l+1)/r2].
It tends to throw the particle outward (away from the origin), just like the centrifugal (pseudo-) force in classical mechanics.
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1926年，埃尔温·薛定谔提 出了薛定谔方程，这个方程 用来描述物理系统中量子态 是怎么样随时间变化的。
schrödinger
13
For a general quantum system, Schrödinger equation is
i
(r , t) [
2
2
V
(r )](r ,
t)
t
2
14
Is quantum mechanics really complicated? 那么，量子力学真的那么复杂吗？ Absolutely not, it is very easy. 当然也不是，其实它是很简单的。
8Байду номын сангаас
In 1900, Planck Put forward a hypothesis that energy is radiated and absorbed in discrete "quanta", or "energy elements", which successfully matched the observed patterns of black body radiation.
Semiconductor 半导体
6
The 21st century will become information age，quantum age! 21世纪将会变为信息时代，量子时代！
iPhone
iPad-3
7
Now we see that quantum mechanics is not far from us. 现在我们知道了量子力学与我们紧密相关。
•
15
In conclusion , there are two points: A . Quantum mechanics is founded by the hypothesis that energy is discrete . B . The core work of quantum mechanics is calculating the Schrödinger equation. So quantum mechanics is very easy. 总而言之，这儿有两点比较重要： A . 量子力学是以能量是不连续为假设建立的。 B . 量子力学的核心工作就是计算薛定谔方程。 所以说，量子力学是很简单的。
• 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。
Einstein
10
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.
大家好！ 我是材料学院的郑泽锐，我的队友有张宇寒、
王亚博、吴起航、李伟、张维、李江、陈鹏辉。
1
Many people have the idea that quantum mechanics is far from us and it is so complex that only geniuses have the ability to know it. 许多人认为量子力学离我们很远，并且只有天才们 才能了解它。
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
9
• in 1905 ，Einstein used Planck’s quantum hypothesis realistically to explain the photoelectric effect.
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。
Bohr
11
The word quantum derives from Latin, meaning “how great” or “how much”. In quantum mechanics, it refers to a discrete unit that quantum theory assigns to certain physical quantities. 量子这个词语来源于拉丁语，意思是“多大”或“多 少”。在量子力学中，它指一些不连续的物理量。
2
Is quantum mechanics far from us? 量子力学离我们真的很远吗？
No,it is just around us. 当然不是，它无处不在！
3
Laser 激光
4
Electron Microscope 电子显微镜
Scanning Picture 扫描图片
5
The theory of semiconductor based on quantum mechanics make information industry flourish. 基于量子力学的半导体理论，使信息产业蓬勃发展。
Light spectrum
12
In 1926, Erwin Schrödinger formulated Schrödinger equation that describes how the quantum state of a physical system changes in time.
16
Until now , we know that both quantum mechanics and relativity theory are absolutely right . But there are some paradoxes between them ，which may be the origin of revolution theory . 迄今为止，我们知道量子力学与相对论都是非常正确的 理论。但是，它们之间还是存在一些不兼容的地方。这 些地方有可能成为未来革命性理论的起点。
Hello , everyone! My name is Zheng Zerui , from School of Materials
Science and Engineering. My teammates are Zhang Yuhan , Wang Yabo ,
Wu Qihang , Li Wei, Zhang Wei, Li Jiang , Chen Penghui.