Introduction to Quantum Mechanics

  • Tarit K. Bose


In 1802 Dalton formulated the law of multiple proportions, which states that if two elements combine in more than one proportion to form different compounds the masses of one of the elements with identical amounts of the second element are in the ratio of integral numbers. In 1833 Faraday found the law of electrolysis as a proof for the existence of an electrical elementary quantum of charge. These discoveries supported the postulation of the particle (atom, molecule) theory of matter. On this basis, during the second half of the 19th century, the mechanical theory of heat was first formulated by Clausius, and was further developed by Maxwell and Boltzmann. Mechanical explanation of the pressure of a gas in a closed vessel, as well as the phenomenon of linear increase of pressure with temperature was possible in this way. In 1811 Avogadro’s hypothesis was formulated, which stated that equal volume of different gases, under the same conditions of temperature and pressure, contain equal number of molecules. In 1869 Mendelejeff and Lothar Meyer developed Periodic Tables. They arranged the elements columnwise on the basis of certain chemical properties, and it was found subsequently, that these properties are dependent on the number of electrons on the outermost orbit around the nucleus of the element. Proceeding from Rayleigh-Jean law of radiation for large wave lengths, and from Wien’s law for short wavelengths, Planck in 1900 combined these two laws semi-empirically and found the famous law of radiation that bears his name. From his analysis, for the first time, the existence of an elementary quantum of radiation was found. A rigorous explanation of Planck’s law was, however, left to Albert Einstein, who in the 1920s applied the results of a statistic developed by an Indian scientist Satyendra Nath Bose to the light particles (photons). In 1905, based on astronomical experiments, Einstein also formulated his theory of relativity and gave for the first time a mass-energy equivalence principle. From the alpha particle scattering experiments in 1906–13, Rutherford concluded that the mass of the atom should almost be totally concentrated around a very dense nucleus around which the electrons move in orbits. The electrons are kept in orbits by a balance between the centrifugal and Coulomb forces. His theory, however, could not explain how the electrons could stay in orbit without any dipole radiation, which would result in their slowing down. An explanation for this was left to the Danish Scientist, Niels Bohr, who, by, Drawing help from another branch of physics, namely, spectroscopy, could explain in 1913 the nature and radius of the electron orbit. This is discussed in detail in the following section.


Diatomic Molecule Wave Mechanics Anharmonic Oscillator Electronic Energy Level Rotational Quantum Number 
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© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Tarit K. Bose
    • 1
  1. 1.ResedaUSA

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