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# Review of EM wave particle by alextt

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• pg 1
```									    Review of EM wave  particle
   EM wave behave as particle:
   Proof:
 Blackbody radiation. Plank proposes ??? to solve ???
problem.
 Photoelectric effect. Einstein proposes ??? in order to
explain ???.
 Compton Scattering. Try to derive Compton Scattering
formula    '    mhc 1  cos  and explain why this is a proof that
e

photon here behaves as particle.
   Energy (EM wave) converts into matter (particle)
   Pair production.
  D: particle
   When photon is a particle, a wave?                            D: wave
Particles (matter) behave as waves
and the Schroedinger Equation

1.   Quiz 9.23.
2.   Topics in particles behave as waves:
   The (most powerful) experiment to prove a wave: interference.
today       Properties of matter waves.
   The free-particle Schrödinger Equation  door to a different
world.
   The Uncertainty Principle.
   The not-unseen observer.
Thur.           The Bohr Model of the atom.
3.   The second of the many topics for our class projects.
4.   Material and example about how to prepare and make a
presentation (ref. Prof. Kehoe)
The (most powerful) experiment to prove a wave:
interference
   Particle or wave, how do I know?
   Particle: scattering. Characterized by mass, position and
momentum.
   Wave: interference. Characterized by wavelength, frequency,
amplitude, phase.
   A double-slit experiment:
   A review of the double-slit experiment in optics. A nice
review article: http://en.wikipedia.org/wiki/Double-
slit_experiment.
   A description of the “thought” experiment: a double-slit
experiment with electrons.
   What is oscillating? The probability density of finding the
particle at a certain location and time.
The Bragg’s Law
   The Bragg’s Law for X-rays scattering off a crystal surface – a
powerful tool to study crystal structures through diffraction.
   Constructive interference when:

2dsin  m
   Where m is the order of interference. m = 1, 2, 3,
The Davisson-Germer experiment
Results:

Confirmed that the
Bragg Law applies
to electrons as well.

Electrons interfere.
Electrons behave
like a wave.

Ref: http://hyperphysics.phy-astr.gsu.edu/Hbase/davger.html#c1
Properties of matter waves

   The de Broglie wavelength of a particle:   h p
   Frequency: f  E h
   (review) Wave number k  2  and
angular frequency:   2 T  2 f
   The h-bar constant:   h 2
 p  k
 E  
   Discussion about the velocity on the board.
The free-particle Schrödinger Equation
   Waves on a string – a mechanical wave
   The wave equation (needs classical mechanics)
 2 y  x,t         2 y  x,t                              y       v
v   2

x 2                 t 2
   A solution: the wave function:                                                            x

y  x,t   Asin  kx  t  with v   k
   The Electromagnetic waves (Maxwell’s equations):
                               
E  0                        B  0
                                    
     B                                  E
E                            B  0 0
t                                   t

E  Asin  kx  t  ˆ
y        with c   k
And the solutions:                           1
B  Asin  kx  t  ˆ
z   and 1 c 2  0 0
c
The free-particle Schrödinger Equation

   The matter waves
 2  Ψ  x,t       Ψ  x,t 
2

                  i
2m x 2                t
   The interpretation of the matter wave function
probability density = Ψ  x,t 
2

   The plane wave
Ψ  x,t   Aei kxt 
Review questions
   How do you understand the wave function of
Ψ  x,t 

   Please review the mechanical waves you learned
in intro level physics course. Refresh yourselve
with wavelength, frequency, amplitude, wave
energy density, wave phase velocity, wave group
velocity.
Preview for the next class
   In chapter 4:
   Section 4.4
   Section 4.5
   Section 4.6
   Questions:
   According to the momentum-position uncertainty principle,
if you know a particle’s position exactly, what precision can
you reach in its momentum measurement?
   What is Bohr’s atom model? In which what is his main
postulate? What is the Bohr radius?