“You can never verify a theory, you can only
verify its predictions!”
: V.Balakrishnan
|
QUANTUM MECHANICS ::
The behaviour of
any classical system takes the system through different states. A ‘state’ is as defined by the
value of the various dynamical variables at that particular instant. In
physics, essentially we are talking about a number, in a measurement, that
quantifies the particular variable.
Quantum
mechanics replaces the dynamical variable with a linear operator, with its
accompanying rules relevant to that mathematical object º OPERATOR.
For dynamical
variables the value of a measurement would have to be necessarily a real
number. The operators that would represent a dynamical variable, hence qualify
to be of a different kind º hermitian operators.
In a classical dynamical system, when we make a series
of measurements of the same property[variable] we expect to get a set of
different values, that may be decided by the measurement process. To get to an
accurate prediction of the actual value we resort to statistical procedures.
This takes care of the gross, systematic & random errors of the
measurement.
In a QM system, it is conceptualised that the system
exists in its various possible allowed states and the act of measurement makes
one such state to show up & the particular value appropriate to that state º the ‘eigen’ state is measured as the
‘eigen’ value of the dynamical variable.
The orthodox position : The particle
was not really anywhere.
It was the act of measurement that forced the particle to ‘take a
stand’.
JORDAN said it plainly, “ Observations not only disturb what is to
be measured, but they produce it . . . . We compel (the particle) to assume a definite
position.
This view [the so-called COPENHAGEN interpretation] is associated
with BOHR and his followers. Among physicists it has always been the most
widely accepted position.
QM gives us a
mathematical procediure to calculate the expected [most probable] value for the
measurement of a particular dynamical variable, given its complete set of
eigenstates. There is an integral definition for the expectation value.
So, in QM we come across a new concept
for a QM system. The uncertainity in the estimation of the canonically
conjugate variables(the state)is not an artefact of the measurement process,
but an inherent characteristic of the system itself, which is described by the
Schroedinger’s equation !
This was
Heisenberg’s valuable contribution to an understanding of QM.
Let
it be said that QM is not completely put as set in this brief outline. This is
just an indicator and would definitely look very intriguing for the
uninitiated! Also, QM itself is deemed to be quite not so complete! What could
be said with a certainity is that it does explain very many phenomena,
especially at microscopic scales and has given all the magic that Physics has
done for this civilisation, with modern technology!
EPILOGUE -
“Anyone who is not shocked by quantum theory has
not understood it.”
-- -- -- NIELS BOHR::
. . .z
The Textbooks
:
1.
A TEXTBOOK OF QUANTUM MECHANICS, P.M.Mathews & K.Venkatesan,
2nd edn.(2010) TMH, India.
2.
QUANTUM MECHANICS, V.Murugan (2014) Pearson, India.
3.
Listen to one of the best Physics teachers on this planet :
http://freevideolectures.com/Course/2669/Quantum- Physics
March 2017 qed n_ln
No comments:
Post a Comment