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波動還是粒子？
─量子世界的奧秘
清華大學物理系
王道維教授
Wave or particle ?
Brief History:
Let’s go back to 100 years ago …..
1684 Isaac Newton, Principa
1768 Stream engine was invented..
1781 I. Kant, Critique of Pure Reason
1783 American independence revolution
1789 French revolution
1831 Electric engine was invented
Science is almost ended in the Newton physics and
Maxwell equations. All others are just details.
From human side, they believe that human beings are good enough
to protect this world and themselves.
However, the first was broken by the discovery of quantum physics in 1905,
while the second hope was broken by World War I in 1914….
Example I: Periodic table
Order ?
Example II: Atom structure
How can atom be stable ?
Example III: Light spectrum
What these lines mean ?
Max. electron energy
Photoelectric effect
What shall we expect ?
Intensity
Max. electron energy
1 2
mvmax  Elight  Ebound
2
Elight  I  t 
1
| A |2 t
2
Frquency
Photoelectric effect
Max. electron energy
Experimental fact
Intensity
Max. electron energy
1 2
mvmax  Elight  Ebound
2
Elight  I  t  N  h
Why ?
Frquency
Max. electron energy
Max. electron energy
Intensity
Intensity
Max. electron energy
Max. electron energy
Frquency
Frquency
Conceptual questions….
What is the meaning of “frequency”, “waveelngth” for a single photon ?
What is the meaning of “quantized energy” for a light wave ?
How could we understand the interference effects between
two light sources by photons ?
Is light a wave or a particle ?
Double slit experiment for electrons
What shall we expect ?
A particle cannot pass two holes at the same time
 It must pass through one of them
 Probability=P1+P2
What is this wavelength about ?
Double slit experiment for electrons
The experimental results
We find interference pattern for “particles” !
An Electron must have to pass both hole at the same time ?
If we want to measure it…..
We find a very surprising result….
Both light and massive particles are not like what we expect
in the ordinary situation….
Their properties cannot be simply understood by our
common sense in the ordinary world….
We need to do the experiment to measure their properties
before we could say about them.
But measurement can changes the results dramatically ….
Is there something wrong ?
Basic concept of Quantum mechanics
1. For an EM wave, we have
E  h  
2. For a massive particle, we have

h
p
3. For a single particle, it is described by a wavefunction,  (r , t )
which describe the probability to find a particle at position r
at time t is P(r , t ) | (r , t ) |2
4. The wavefunction follows the Schrodinger equation:
 ( x, t )   2  2 ( x, t )
i

 V ( x) ( x, t )
2
t
2m
x
5. One could not know anything (but probability) about a single event
But not only we do not like it….
A. Einstein: God does not play dice with the universe.
Gradually we used to it….
R.P. Feynman:
I think it is fair to say that no
on really understand quantum
mechanics…. We just know
how to calculate it….
Quantum tunneling:
STM
STM image:
STM
Matter wave to understand this world…..
Standing wave gives discrete
energy level !
Pauli exclusion principle then
explains the preriodic table !
E=hv makes the discrete energy
level to be observed by discrete
light spectroum.
Visible quantum world…..
Quantum world is much more dramatic than
what people could image in ordinary life !
What is more surprising is : we human
beings can “understand” this strange world ?!