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定态薛定谔方程
将上式代入一般薛定谔方程并除以上式得
势能函数U=U(r)不随时间变化, 则波函数可以分离变量
定态薛定谔方程
等式两边相互无关，故应等于与r,t都无关的常数
设此常数=E
概率密度与
时间无关
即在定态下概率分布不随时间改变，这正是定态这一名称的由来。
概率：
定态，能量确定态，能量本征态，所有物理量的平均值（概率平均）不随时间改变
定态：能量确定，能量本征态，特殊态；
算符作用到波函数上等于一个数乘这个波函数，则称这个波函数是该算符的本征函数，这个数值称为该算符的本征值，这个方程称为该算符的本征方程。
定态薛定谔方程的意义：
对波函数进行某种运算或作用的符号称为算符。
算符，本征值，本征函数
定态薛定谔方程式也称为哈密顿算符的本征方程，或能量算符的本征方程。
定态,迭加态，本征态，态指标
设二能级原子有两个本征态 和 ，分别具有能 量本征值 。能量本征态即定态
多个定态叠加，叠加态。态矢量
多个定态之间，线性无关，一个定态不可能有另一个定态的成分，正交，归一
标记此态：本征波函数，态指标
如果原子处在叠加态,在叠加态中，各个本征态以
一定的概率出现,
也叫非本征态，处于该态粒子的能量没有确定的实验测量值与它对应，需求能量算符的平均值。
二能级，两定态，基态和激发态，彼此正交归一，表示如下
完全处于第一个定态
完全处于第二个定态
两个定态作为态矢量的基矢
上述叠加态表示原子以概率
处在基态
同时以概率
处在激发态
基态和激发态构成二能级原子状态的一组矢量空间的基矢，也叫能量本征态。二能级原子的任一其他的态可以按这基矢展开。
一般来说，二能级原子，任一状态为
归一性要求
birthday of quantum mechanics
Max Planck (1858-1947)
Nobel Prize 1918
14 December 1900
Planck (age 42)
suggests that
radiation is quantized
E = hn
h = 6.626x10-34 J s
1897 Thompson (age 41)
Nobel Prize 1906
measures the electron
"plum pudding" model
1905 Einstein (age 26)
proposes the photon
1911 Rutherford (age 40)
infers the nucleus
Status of physics
Albert Einstein (1879-1955)
Nobel Prize 1921
1913, Bohr (age 28)
constructs a theory of atom
1921 Bohr Institute opened
in Copenhagen (Denmark)
It became a leading center
for quantum physics
(Pauli, Heisenberg, Dirac, …)
Niels Bohr (1885-1962)
Nobel Prize 1922
old quantum theory
旧量子论
matrix formulation of quantum mechanics
Werner Heisenberg (1901-1976)
Nobel Prize 1932
1925 at G ttingen (Germany)
M. Born (age 43) W. Heisenberg (age 23) P. Jordan (age 22)
Max Born (1882-1970)
Nobel Prize 1954
wavefunction formulation of quantum mechanics
Erwin Schr dinger (1887-1961)
Nobel Prize 1933
1923 De Broglie (age 31)
matter has wave properties
Louis de Broglie (1892-1987)
Nobel Prize 1929
1926 Schr dinger (age 39)
Schr dinger equation
1926 Erwin Schr dinger in Austria
Carl Eckert (age 24) in America
Proved: wave mechanics = matrix mechanics
(Schr dinger and Heisenberg theories equivalent mathematically)
Schr dinger's wave mechanics eventually became the
method of choice, because it is less abstract and easier
to understand than Heisenberg's matrix mechanics
Neumann (mathematician) invented operator theory
Largely because of his work (publish his book in 1932),
quantum physics and operator theory can be viewed as
two aspects of the same subject.
wave mechanics = matrix mechanics
Paul Dirac (1902-1984)
Nobel Prize 1933
1925 Pauli (age 25)
Pauli exclusion principle
Wolfgang Pauli (1900-1958)
Nobel Prize 1945
1928 Dirac (age 26)
Dirac equation (quantum+relativity)
M. Curie
Lorentz
Compton
Solvay
Brillouin
Deby
The 5th Solvay Conference in 1927
Held in Belgium,
the conference was attended by the world's most notable physicists
to discuss the newly formulated quantum theory.
A number of scientists, including Schr dinger, de Broglie,
and most prominently Einstein, remained unhappy with the
standard probabilistic interpretation of quantum mechanics.
"Anyone who has not been shocked by
quantum physics has not understood it."
- Niels Bohr
It was applied to atoms, molecules, and solids.
It solved with ease the problem of helium
It was used to explain chemical bonding
It resolved various questions: structure of stars,
nature of superconductors,
:
Even today it is being applied to new problems.
applications of quantum mechanics
Quantum mechanics has been tremendously successful !
事实上，不仅仅是能量算符，任何一个算符的本征态都是一组正交完备集，可以作为基矢来表达所有算符的本征态矢量
态矢量作用何在？
求F的解本征方程！
用H的本征矢作为基矢来表示的本征方程！
矩阵表示，表象变换

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