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| Some of the physicists who made early contributions to quantum mechanics (left to right, top row first): Neils Bohr, Albert Einstein, Max Planck, Wolfgang Pauli, Werner Heisenberg and Erwin Schrödinger. |
By the end of the nineteenth
century, physics was mainly consisted of classical (or Newtonian mechanics), classical
(or Maxwellian) theory of electrodynamics and Thermodynamics. Together, these
three branches of physics were able to explain almost all of the phenomena
observed in nature. For instance, the optical phenomena like reflection,
refraction, snell’s law, etc. were very well accounted for by classical
electrodynamics. Behaviour of gases in various conditions were explained by
thermodynamics. Problems involving motion of celestial bodies could be tackled
effectively and very accurately by classical mechanics. More general topics
such as Elastic properties, certain electrical and thermodynamic properties of
materials could be explained satisfactorily by combining results of mechanics,
electrodynamics and thermodynamics. The overall structure of physics seemed
complete and impeccable and capable of explaining all the known physical
phenomena accept a few pending issues which, as was thought, could be accounted
for in due course of time. But as always happens, nature had a whole bag of
surprises of the physicists.
Some of the experiments conducted
in the late nineteenth century showed considerable disagreement between the
experimentally observed facts and theorectical predictions. Most prominent of
them are Black Body Radiation, Photoelectric effect, specific heat capacity of
metals, Precession of Mercury’s orbit, stellar abberation, atomic stability and
atomic spectra and the famous Michelson’s interferometer experiment which put
the Maxwell’s ambiguous ether in big trouble. No amount of efforts could patch
up these gaps between the experimental and theoretical results. People, then,
started realising that the then existing framework of classical physics was not
sufficient and still incomplete to account for these problems and new laws have
to be discovered. The final blow to the already trembling classical physics was
given by Max Planck and Albert Einstein at the advent of 20th century which
marked the end of nearly 300 years of unchallenged classical era for good.
In the year 1900, Max Planck came
up with a solution for one of the most perplexing problems of that time - Black
Body Radiation. The problem was as follows : at a particular temperature, a
black body emits radiation of all frquencies but with different energy densities.
The relation between the frequency of emitted radiation and corresponding
energy density could not be explained by the then existing principles of
thermodynamics and classical electrodynamics. So, Planck did something similar
to what students usually do in lab - if you do not get the required results,
manipulate your calculations to fit the experimental results or vice versa. Out
of the blue he made an ad hoc assumption - the radiation could be absorbed or
emitted only in the form of discrete packets or quantas, each quanta having
energy equal to hν where ν is the frequency of radiation and h is
a universal constant known as Planck’s constant. He fixed the value of h such
that the theoretical resultsare in accord with experimental
observation. The plot he obtained this way coincided with the experimentally
determined plot.
This put a big question mark on
the credibility of classical electrodynamics which asserts that radiation has
characteristics of waves. But the problem was that Planck, at that time, did
not have any logical explanation for making such an assumption and it was
impossible to discard well established classical electrodynamics on such
grounds.
Then came Einstein to make the
situation worse for classical physics. In 1905, he published three
ground-breaking papers which shook the very foundations of classical theories.
One of the papers was on Photoelectric effect where he showed that radiation is
not only absorbed/emitted in the form of quantas of definite energy but also
propagates in the form quantas, known as Photons of energy hν. This settled the
dispute once and for all as it was proved that radiation consisted of
corpuscular photons which completely contradicts the wave picture of radiation
- the premise on which the whole classical electrodynamics is based.
His other paper on Special Theory
of Relativity was a nightmare for classical mechnics and electrodynamics. One
of the most fundamental assumptions on which the whole classical physics is
based is that time is absolute. This means that when you measure time using
clocks that seperated in space and/or have a relative motion with respect to
each other, the clocks would read the same time i.e. time is the same
everywhere in the universe and is thus absolute. Einstein proved exactly
opposite of this that time is not absolute but relative. What time you measure
depends on where are you measuring it from. Time differs from place to place
and relative motion. This made the entire classical
physics crumble down.
Now that it was apparent that the
existing framework of classical physics was obsolete and insufficient to
explain many physical phenomena, people started looking for other alternative
and abstract solutions to such problems. Rutherford, by his famous scattering
experiment using alpha particles and a thin gold leaf, showed that atoms
consist of a small but heavy positively charged centre called nucleus and rest
of the space being occupied by negatively charged electrons but majority of it
being empty. Classical electrodynamics failed miserably in explaining the
stability of such electron -nucleus model of atom. It required the electrons to
dissipate the energy gradually while moving about the nucleus and eventually
collapse into the nucleus. This kind of behaviour would make an atom unstable
contrary to what is actually observed in nature.
Another hurdle for classical
physics was the characteristic line spectra exhibited by the atoms of different
elements. There was no plausible explanation, in the realms of classical
physics, as to why should atoms exhibit such a line spectra and not a
continuous one. This problem baffled everyone until 1913 when Neils Bohr came
in with his model of hydrogen atom.
He adopted similar method to what
Planck did - manipulate! - to explain the Hydrogen spectrum. He coined one very
important postulate – quantisation of Angular Momentum - which states that the
angular momentum of an electron orbiting the nucleus is quantised such that it
is integral multiple of
Such
electrons were supposed to be in stationary
states with definite energy values. These electrons are in stable configuration
and do not dissipate energy and hence do not collapse into the nucleus. When an
electron makes a transition from one state to another, it absorbs/emits energy
equal to the difference of electron’s energies in both the states involved in
the transition.
The results of the Bohr’s model
of hydrogen atom were in complete agreement with the experimental observations.
This was a tremendous success with only one problem - the ad hoc assumption of
the quantisation rule.
In 1923, Compton made a yet
another very important discovery. He scattered X-rays with electrons and
confirmed that X-ray photons behave like particles with momenta
where ν is the frequency of the X-rays used.
The efforts of Planck, Einstein,
Bohr and Compton confirmed that at microscopic scale electromagnetic radiation
exhibited corpuscular nature. At this scale, the classical physics fails
quantitatively, qualitatively as well as conceptually.
So far, it had been found that
radiation exhibited particle-like properties in the sense that they consist of photons which are quantised. There was
yet another startling discovery to be made.
In 1923, de Broglie introduced
the concept of matter waves. He
postulated that associated with a particle of momentum p there are waves of
wavelength
These waves are known as matter
waves4. Thus he asserted that not only does radiation exhibit particle-like
nature but particles also display wave-like properties. This concept was
confirmed in 1927 by Davison and Germer. They showed that an interference
pattern could be produced by impinging electrons of definite momentum on a
crystal, in a similar way as X-ray diffraction pattern of a crystal is
obtained.
Though the models suggested by
Planck (1900) and Bohr (1913) produced results in agreement with the
spectroscopic experiments, they were, however, based on arbitrarily made
assumptions and postulates. There was a need of a consistent theory which would
account for these abstract assumptions as well as capable of predicting yet
unexplored physical phenomena. This was done independently by Heisenberg and
Schrodinger in 1925. They could successfully merge all the experimental
findings of twenty five years (1900 - 1925) into a refined theory known as Quantum
Mechanics. At that time there were two formulations of quantum mechanics : one
known as matrix mechanics due to
Heisenberg and the other known as wave
mechanics due to Schrodinger.
Matrix mechanics was developed by
Heisenberg in 1925 to describe the atomic structure starting from the
characterisctic atomic line spectra. Heisenberg based his theory on the
observation that only discrete values of energy exchange was allowed between
microscopic systems, as was apparent from Planck’s quantization of
radiation, Einstein’s photoelectric effect and Bohr’s model of the hydrogen
atom. He expressed dynamical quantities such as position, momentum, angular
momentum and energy in the form of matrices and described the dynamics of
microscopic systems by an eigenvalue equation.
Other formulation - wave
mechanics, developed by Schrodinger in 1926 is a generalisation of the de Broglie hypothesis. In contrast to
matrix mechanics, Schrodinger described the dynamics of microscopic systems by
means of a wave equation known as Schrodinger
equation (it is a differential equation). The solution to this equation
yields the so called wave function and
energy spectrum of the system under
study. In 1927, Max Born came up with his probabilistic interpretation of wave
mechanics where he interpreted the square moduli of wave functions as probability densities. Heisenberg
actually actively opposed the Schrodinger’s wave mechanics.
These two seemingly different
formulations were shown to be equivalent by P. A. M. Dirac. He single handedly
constructed a more general formulation of quantum mechanics which deals with
abstract objects such as state vectors (kets and bras) and operators. The
representation of Dirac’s formalism in a continuous basis, known as position or
momentum representation, gives the Schrodinger’s wave mechanics. Whereas,
representing it a discrete basis yields Heisenberg’s matrix mechanics. Thus,
Dirac’s formalism is a more general theory of quantum mechanics from which wave
and matrix formulations can be obtained.
In 1928, Dirac achieved yet
another impressive feat by successfully combining special relativity with
quantum mechanics and gave birth to a more general, consistent and elegant
theory known as relativistic quantum mechanics. He obtained a relativistic
equation describing the motion of an electron and predicted the existence of an
anti-particle - the positron, with charge opposite to that of an electron. This
theory introduced more abstract concepts like Dirac sea which explained the
pair production and annihilation process. The positron was discovered in an
experiment four years later in 1932.
One of the many important achievements
of quantum mechanics was that it unified physics with chemistry and biology.
All the chemical processes like reactions, energy involved in reactions, bond
formation, concepts like hybridisation, stability of bonds, etc. are readily
explained by quantum mechanics. Thus chemistry and biology are well explained
on the fundamental level and consists mostly of finding, explaining,
manipulating and fabricating new chemical processes (usually pertaining to
existing social and industrial problems).
The development of physics did
not stop here. The efforts of people like Landau, Pomeranchuk, Murray Gellman,
Feynman, Abdus Salam, etc. to contruct a unified theory which would be capable
of explaining all the observed physical phenomena led to the development of the
most consistent, beautiful and intricate (as well) theory known as Quantum
Electrodynamics. It is the most accurate known theory till date and unifies
three fundamental forces of nature : the electromagnetic force, the weak force
and the strong force. Any phenomenon, not involving the force of gravity, can
be explained with this theory. The ultimate goal of physics is to achieve a
unified theory, containing all the four fundamental forces of nature including
gravity, capable of explaining every observed physical process as well as
predict other unexplored and unthought-of phenomena. But this is not an easy
task. It has defied the attempts of the giants like Einstein, Feynman, etc. and
has been the subject of fascination for all the theoretical physicists and the
current topic of research. Achievement of this unification would complete our understanding
of the nature.
For a more detailed account, interested readers can refer the following link
http://www.slac.stanford.edu/pubs/beamline/30/2/30-2-carson.pdf
Credit for the picture:
http://phys.org/news163670588.html
Next post : Fundamental Of Quantum Mechanics
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