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5/22/2011
1
Physics 1C
Lecture 28D
"I ask you to look both ways. For the road to a
knowledge of the stars leads through the atom;
and important knowledge of the atom has
been reached through the stars."
Sir Arthur Eddington
Outline
An Interpretation of QM
Particle in a box
Atomic physics
Emission spectra
Absorption spectra
An Interpretation of QM
Probability
V
N
I
V
2
IE
Particle interpretation:
Wave interpretation: the intensity is proportional to the
square of the electric field amplitude:
2
Probability
V
E
Combine the two points of view:
For EM radiation, the probability of finding a particle
associated with this radiation is proportional to the
square of the amplitude of the associated EM wave.
The particle is the photon in this case.
The amplitude of the wave is called the
probability
amplitude
or the
wave function
. The symbol is
y
.
An Interpretation of QM
The probabilistic interpretation of the wave function
was suggested by Max Born in 1928.
Erwin Schrödinger proposed a wave equation which
describes the manner in which the wave function
changes in space and evolves with time.
This equation is a key element in the theory of
quantum mechanics.
If
represents a single particle, 

2
is the relative
probability per unit volume that the particle will be
found at any given point in the volume.


2
is called the
probability density.
Particle in a Box
Let’s consider a particle confined to a one
dimensional region in space.
Following the quantum mechanics approach, we
need to find an appropriate wave function to describe
the motion of the particle.
Because of the walls, the
probability of finding the
particle outside the box is
zero.
This means that
(
x
)=0
for
x
0 and for
x
L
.
When the particle is inside the
box, the potential energy of the
system is constant.
Particle in a Box
2
( )
sin
x
xA
=
We can define the potential energy to be infinitely
large outside the box.
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 Spring '11
 Wethien

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