T
HE
I
NTERACTION OF
R
ADIATION AND
M
ATTER
:
S
EMICLASSICAL
T
HEORY
I.
R
EVIEW OF
B
ASIC
Q
UANTUM
M
ECHANICS
: C
ONCEPTS
, P
OSTULATES AND
N
OTATION
:
At the outset, let us, briefly, reconsider why quantum mechanics is necessary?
•
Forces known in classical electrodynamics cannot account for the remarkable
stability of atoms and molecules.
•
Disturbed dynamic systems radiate only frequencies which may be expressed as
differences between certain values (Ritz's Combination Law of Spectroscopy).
1
•
All physical systems 
viz.
material "particles" and electromagnetic fields  exhibit
waveparticle duality

i.e.
to explain particular observations the system must in
some instances be modeled as a particle and in others as a wave.
•
There is a limit below which the disturbance associated with a observation is not
negligible and, thus, there is an unavoidable
indeterminacy
in the prediction of
observed results.
To proceed, we recall an ancient comment of P. A. M. Dirac:
2
"Quantum mechanics…requires the states of a dynamic system and the dynamical
variables to be to be interconnected in quite strange ways that are unintelligible from
the classical standpoint.
The states and dynamic variables have to be represented by
mathematical quantities of different natures from those ordinarily used in physics"
Following the Master we begin with the general quantum mechanical
principle of
superposition of states
.
To quote him once more:
1
According to classical theory, a disturbed system should radiate certain fundamental frequencies and their
harmonics.
Each fundamental frequency would be associated with one of the systems degrees of freedom.
2
P. A. M. Dirac,
The Principles of Quantum Mechanics
(Revised fourth edition), Oxford University Press (1967).
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T
HE
I
NTERACTION OF
R
ADIATION AND
M
ATTER
: S
EMICLASSICAL
T
HEORY
P
AGE
2
R. Victor Jones, March 6, 2000
"The nonclassical nature of the superposition process is brought out clearly if we
consider the superposition of two states, A and B, such that there exists an
observation which, when made on the system in state A, is certain to lead to one
particular result,
a
say, and when made on the system in state B is certain to lead to
some different result,
b
say.
What will be the result of the observation when made
on the system in the superposed state? The answer is that the result will be
sometimes
a
and sometimes
b
, according to a probability law depending on the
relative weights of A and B in the superposition process.
It will never be different
from both
a
and
b
.
The intermediate character of the state formed by
superposition thus expresses itself through the probability of a particular result
for an observation being intermediate between the corresponding probabilities
for the original states, not through the result itself being intermediate between
the corresponding results for the original states
.
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 Winter '08
 Staff
 Vector Space, Force, Radiation, R. Victor Jones

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