The important discoveries and events that occurred in the development of quantum mechanics may be ordered as follows: Blackbody radiation formulated by Max Planck in 1901. Photoelectric effect interpreted by Albert Einstein in 1905. Model of the atom proposed by Ernest Rutherford in 1911. Quantum theory of atomic spectra developed by Niels Bohr in 1913. Photon–electron scattering experiments done by Arthor Holly Compton in 1922. Exclusion principle proposed by Wolfgang Pauli in 1925. Matter waves proposed by Prince Louis Victor de Broglie in 1925. Wave equation proposed by Erwin Shrödinger in 1926. Electron diffraction experiments done by Clinton Joseph Davisson and L.H. Germer in 1927. Uncertainty principle proposed by Werner Karl Heisenberg in 1927. Interpretation of the wave function done by Max Born in 1927. Relativistic wave equation proposed by Paul A. M. Dirac in 1928.
The important discoveries and events that occurred in the development of quantum mechanics may be ordered as follows: Blackbody radiation formulated by Max Planck in 1901. Photoelectric effect interpreted by Albert Einstein in 1905. Model of the atom proposed by Ernest Rutherford in 1911. Quantum theory of atomic spectra developed by Niels Bohr in 1913. Photon–electron scattering experiments done by Arthor Holly Compton in 1922. Exclusion principle proposed by Wolfgang Pauli in 1925. Matter waves proposed by Prince Louis Victor de Broglie in 1925. Wave equation proposed by Erwin Shrödinger in 1926. Electron diffraction experiments done by Clinton Joseph Davisson and L.H. Germer in 1927. Uncertainty principle proposed by Werner Karl Heisenberg in 1927. Interpretation of the wave function done by Max Born in 1927. Relativistic wave equation proposed by Paul A. M. Dirac in 1928.
This chapter starts with the historical development of quantum mechanics and explanations of key concepts behind fundamental discoveries such as Planck's hypothesis, the photoelectric effect, Bohr's atomic model, Compton scattering, the de Broglie hypothesis, the Pauli exclusion principle, the Schrödinger equation, Heisenberg quantum mechanics and the uncertainty principle, the Born interpretation of wave function, the Davisson and Germer experiment, and Dirac relativistic quantum mechanics, which made important contributions to the foundation of modern quantum mechanics. Concepts like the particle properties of radiation, the wave properties of matter, quantized energy and momentum, and the idea that one can no longer know exactly where a single particle like an electron is at any instant of time are brought out clearly through this chapter. A list of important quantum mechanical parameters along with solved examples and unsolved exercises on the key concepts are included towards the end.
Many breakthrough experimental discoveries in the realm of physics are described, notable among them being Young’s double-slit experiment, Davisson and Germer experiment on electron diffraction, and Crompton scattering of X-rays or γ -rays. Also explained are revolutionary theories such as Planck’s quantum hypothesis, Bohr’s model of atomic structure, and Einstein’s interpretation of photoelectric effect, which laid down the foundations of quantum theory. Wave-particle dualism is epitomized in cornerstone theories namely de Broglie’s hypothesis and Heisenberg’s uncertainty principle. Surprisingly, the old notion of treating electrons as particles moving in an electric field works satisfactorily in many everyday-life applications but leads to serious errors at the nanoscale where the wave picture of electrons salvages our understanding of matter and energy. Electrons can act as particles or waves. The wave picture has its origins in the quantum theory.
We tried to introduce the idea of quantization in Chapter 9 as a completion of a one semester course. However, we skipped over some really interesting events in the history of Science between 1900 and 1913 when Bohr derived the quantized energy of the H atom. First we want to carry out the 1901 Planck derivation of the formula for blackbody radiation [1]. Many texts just show the curve, write e¼ hn, and move on. As a student, this author found that limited explanation very frustrating since energy quantization is a fundamental concept. Even among graduate texts in quantum mechanics, we are aware of only one that does the complete treatment which we will draw upon for the mathematics [2] but supplement with a narrative that we have found helpful to students over the years. Then in 1905, Albert Einstein (1879-1955), one of the most influential scientists of all time, gave an explanation of the photoelectric effect [3] for which he received the Nobel Prize in 1921. Even reducing our list to essential topics, we need to discuss the Davisson-Germer experiment [4]. The photoelectric effect introduces the idea that light waves can act as particles while the Davisson-Germer experiment showed that particles can act like waves and confirmed the De Broglie equation [5]. However, you can be assured that it will not be as difficult as you might have anticipated and if you can absorb the meaning of just these three key experiments you should be able to begin thinking in terms of quantum mechanics! Despite our slow historical development, this is 2010 and we have to get to the twenty-first century somehow!
At the beginning of the twentieth century, it became clear that microscopic particles do not obey Newton's laws of classical mechanics. The idea of light quanta was at odds with the established wisdom that light is a wave phenomenon, of course, but no other explanation of the photoelectric effect seemed possible. The next step in the development of quantum mechanics was taken by Niels Bohr, who introduced postulates about the discreteness of the energy of the bound electrons in an atom similar to the discreteness of the energy of light quanta. Modern quantum mechanics was founded by Werner Heisenberg, Max Born, Erwin Schroedinger, Paul Adrian Maurice Dirac, Wolfgang Pauli, Enrico Fermi, and others. In quantum mechanics, it is in general fundamentally impossible to determine the exact outcome of an experiment; one can only determine the probability of any given outcome.
Abstract In addition to recounting some contemporary scientific history, Chapter 6 describes the hypothesis that matter, like light, can display wavelike properties, and the creation of the various formulations of quantum mechanics. That matter could have a wavelength was proposed in 1924 by Louis de Broglie, who presented a specific formula for calculating it, one that was verified experimentally in 1927. However, de Broglie’s hypothesis was overshadowed by the creation of three versions of quantum mechanics in 1925/26. The first, denoted matrix mechanics, was proposed by Werner Heisenberg. It was quickly and successfully applied by Wolfgang Pauli to the hydrogen atom. Paul Dirac introduced the next version, which was followed by that of Erwin Schrödinger via a wave equation whose solutions, denoted wave functions, were soon interpreted byMax Born to be related to the probability that certain outcomes or events will occur: classical-physics determinism was thereby removed from quantum mechanics.
Abstract This chapter examines some crucial experiments and basic principles of quantum mechanics that have strongly influenced the development of quantum theory in its modern form: starting from Planck’s law of black-body radiation and its derivation using the quantization of energy; Einstein’s photon hypothesis for the puzzle presented by the photoelectric effect and its test via the Millikan experiment; the Compton effect; Bohr’s theses for the structure of the hydrogen atom and the complementarity of waves and particles i.e., the wave-particle duality, culminating in de Broglie’s ideas for matter waves and their confirmation in the Davisson-Germer experiment for electron diffraction from a crystal; Heisenberg’s uncertainty principle for position and momentum as well as for energy an time; the famous double-slit experiment and Born’s probability interpretation, and finally the provocative thought experiment of Schrödinger’s cat