QM-Lecture Notes-05 Rise of Quantum Mechanics

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The aim of this unit is to motivate

  •  superposition of states and the need for vector spaces to describe states of quantum systems.
  • indeterminacy and introduction of probability in quantum mechanics as a consequence of superposition principle.
  •  uncertainty principle and simultaneous measurement.

In \(\S2\) important  developments that led to the birth of quantum mechanics (1900-1926)   are  sketched. The developments, before the birth  of quantum mechanics in 1926, collectively known as ``Old Quantum Theory'' were replaced by the new mechanics. This is not aimed at providing historical developments in full detail which in any case are available for interested  readers. We aim to provide motivation and to encourage the reader to go to the references where authentic account of historical facts can be found.

The wave particle duality had important consequences for classical concepts and the way we think of physical systems. These are summarised in  \(\S 3\);

An analysis of thought experiments, \(\S 4\), on measurement of position and momentum leads to formulation of  uncertainty principle on simultaneous measurement of position and momentum.

An analysis of thought experiments on polarisation of photons in $\S  5.1$  and on electron interference is presented in $\S 5.2$. This discussion highlights the need for superposition of states and indeterminacy of the classical theory. The thought experiments suggest introduction to probabilities in quantum theory in way that works differently as compared to classical physics.

The postulates of quantum mechanics are stated in \(\S 6\).  You must bear in mind that this is only a beginning and a full understanding of postulates will come slowly through discussion and applications.

The section  $\S 7$  highlights the  changes that are required from the classical concepts. The beginners must note these changes carefully as the older concepts and ideas have to be given up. Some of the early successes are listed in \(\S8\)


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