Transcript powerpoint

The Quantization
of the
Angular Momentum
1
Quantization of the absorption
The Phenomenon
The Model
In the gas phase discrete
absorption lines appear in the
spectral reagions where in the
liquid phase the absorbtion is
continuously.
In the gas phase, unlike the liquid
phase there are additional free
translation and rotation degrees of
freedom. The rotation* is the one
responsible for the absorption
lines.
CH3I(g)
CH3I()
* The rotation is the degree of freedom of a free particle, and therefore
has a continuous energy (k is continuous)
2
A free Particle on a Ring – a Classical picture
A system composed of two particles, which are connected
by a rigid rod of length r. The particles perform a rotating
motion on a plain. This system is equivalent to a single
particle of a reduced mass µ, moving around the center of
mass, with a constant radius.
z
(-)I
y
(+)CH
3
x
3
The Quantum Mechanics Postulates for a Free
Particle on a Ring
1. (The tools of the game) The system state can be described by a
wavepacket, (the board of the game) pertaining to the space of
continuous functions in angle :
2. (The rules of the game) For each component in the wavepacket
the following is true:
3. (The interface) the measurement outcome has the following
probability of finding the particle in an angle :
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Postulates I: Quantization of m
To meet the continuity condition it is possible to
include in the wavepacket only functions whose
quantum number m is an integer
m=1
m=1.5
m=2
5
Postulates II: Quantization of the Angular
Momentum and the Energy
The dispersion ratio is selected to ccorrospond to the
classical limit of h:
To each wave
are attributed
the angular momentum
and the kinetic energy
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Postulates III : Dipole Moment
In a single wave the charge distribution is symmetrical. In
superposition of two waves it is possible to obtain an
asymmetrical distribution of the charge, which is equivalent to
an existence of a Dipole Moment
y
y
y

x
+

x
=

x
7
Quantization of the Light Absorption
A rotating Dipole Moment is capable of exchanging energy with
a radiation field in its self frequency (the resonance principle.)
The frequency of an envelope changing in a superposition is:
And therefore:
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