User:Johnjbarton/sandbox/introduction to quantum mechanics
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History
Maxwell's unification of electricity, magnetism, and even light in the 1880s lead to experiments on the interaction of light and matter. Some of these experiments had aspects which could not be explained. Quantum mechanics emerged in the early part of the 20th century from efforts to explain these results.[1]
Evidence of quanta from the photoelectric effect
The seeds of the quantum revolution appear in the discovery by JJ Thomson in 1897 that cathode rays were not continuous but "corpuscles" identical to electrons. Electrons had been named just six years as part of the emerging theory of atoms. In 1900, Max Planck, a conservative physicist unconvinced by the atomic theory, discovered that he needed discrete entities like atoms or electrons to explain blackbody radiation.[2]
Hot objects radiate heat; very hot objects – red hot, white hot objects – all look similar when heated to the same temperature. This temperature dependent "look" results from a common curve of light intensity at different frequencies (colors). The common curve is called blackbody radiation. The lowest frequencies are invisible heat rays – infrared light. White hot objects have intensity across many colors in the visible range. Continuous wave theories of light and matter cannot explain the blackbody radiation curve. Planck spread the heat energy among individual "oscillators" of an undefined character but with discrete energy capacity: the blackbody radiation behavior was then correct.
At the time, electrons, atoms, and discrete oscillators were all exotic ideas to explain exotic phenomena. But in 1905 Albert Einstein proposed that light was also corpuscular, consisting of "energy quanta", seemingly in contradiction to the established science of light as a continuous wave, stretching back a hundred years to Thomas Young's work on diffraction.
His revolutionary proposal started by reanalyzing Planck blackbody theory, arriving at the same conclusions by using the new "energy quanta". Einstein then showed how energy quanta connected to JJ Thomson's electron. In 1902, Philipp Lenard directed light from an arc lamp onto freshly cleaned metal plates housed in an evacuated glass tube. He measured the electric current coming off the metal plate, for higher and lower intensity of light and for different metals. This is the photoelectric effect. Lenard showed that amount of current – the number of electrons – depended on the intensity of the light, but that the velocity of these electrons did not depend on intensity. The continuous wave theories of the time would predict that more light intensity would accelerate the same amount of current to higher velocity contrary to experiment. Einstein's energy quanta explained the volume increase: one electron is ejected for each quanta: more quanta mean more electrons.
Einstein then predicted that the electron velocity would increase in direct proportion to the light frequency above a fixed value that depended upon the metal. Here the idea is that energy in energy-quanta depends upon the light frequency; the energy transferred to the electron comes in proportion to the light frequency. The type of metal gives a barrier, the fixed value, that the electrons must climb over to exit and be measured.
Ten years elapsed before Millikan's definitive experiment[3] verified Einstein's prediction. During that time many scientists rejected the revolutionary idea of quanta.[4] But Planck's and Einstein's concept was in the air and soon affected other theories.
| Light intensity increase | Light frequency increase | |
|---|---|---|
| Experiment | current increase | energy increase |
| Continuous Theory | X energy increase | ? |
| Quantum Theory | ✔ current increase | ✔ energy increase |
Quantization of bound electrons in atoms
Experiments with light and matter in the late 1800s uncovered a reproducible but puzzling regularity. When light was shown through purified gasses, certain frequencies (colors) did not pass. These dark absorption 'lines' followed a distinctive pattern: the gaps between the lines decreased steadily. By 1889, the Rydberg formula predicted the lines for hydrogen gas using only a constant number and the integers to index the lines. The origin of this regularity was unknown. Solving this mystery would become quantum mechanics first major victory.
Throughout the 19th century evidence grew for the atomic nature of matter. With JJ Thomson's discovery of the electron in 1897, scientist began the search for a model of the interior of the atom. Thomson proposed negative electrons swimming in a pool of positive charge. Between 1908 and 1911, Rutherford showed that the positive part was only 1/3000th of the diameter of the atom.
Models of "planetary" electrons orbiting a nuclear "Sun" were proposed, but in 1913 Neils Bohr and Ernest Rutherford connected the new atom models to the mystery of the Rydberg formula: the orbital radius of the electrons were constrained and the resulting energy differences matched the energy differences in the absorption lines. This meant that absorption and emission of light from atoms was energy quantized: only specific energies that matched the difference in orbital energy would be emitted or absorbed.
Trading one mystery – the regular pattern of the Rydberg formula – for another mystery – constraints on electron orbits – might not seem like a big advance, but the new atom model summarized many other experimental findings. The quantization of the photoelectric effect and now the quantization of the electron orbits set the stage for the final revolution.
Quantization of matter
In 1922 Otto Stern and Walther Gerlach demonstrated that the magnetic properties of silver atoms do not take a continuous range of values: the magnetic values are quantized and limited to only two possibilities.[5] Unlike the other then known quantum effects, this striking result involves the state of a single atom.[1]: v2:130
In 1924 Louis de Broglie proposed that electrons in an atom are constrained not in "orbits" but as standing waves. In detail his solution did not work, but his hypothesis – that the electron "corpuscle" moves in the atom as a wave – spurred Edwin Schrodinger to develop a wave equation for electrons; when applied to Hydrogen the Rydberg formula was accurately reproduced. In 1928 Paul Dirac published his relativistic wave equation simultaneously incorporating relativity, predicting anti-matter, and providing a complete theory for the Stern-Gerlach result. These successes launched a new fundamental understanding of our world: quantum mechanics.
Planck and Einstein started the revolution with quanta that broke down the continuous models of matter and light. Twenty years later "corpuscles" like electrons came to be modeled as continuous waves. This result came to be called wave-particle duality, one iconic idea along with the uncertainty principle that sets quantum mechanics apart from older models of physics.
Quantum radiation, quantum fields
Around 1926 Einstein's "energy quanta" got a new name: it came to be called a "photon".[6]
- ^ a b Whittaker, Edmund T. (1989). A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 (Repr ed.). New York: Dover Publ. ISBN 978-0-486-26126-3.
- ^ Baggott, J. E. (2013). The quantum story: a history in 40 moments (Impression: 3 ed.). Oxford: Oxford Univ. Press. ISBN 978-0-19-965597-7.
- ^ Millikan, R. A. (1916-03-01). "A Direct Photoelectric Determination of Planck's " h "". Physical Review. 7 (3): 355–388. doi:10.1103/PhysRev.7.355. ISSN 0031-899X.
- ^ Pais, A. (1979-10-01). "Einstein and the quantum theory". Reviews of Modern Physics. 51 (4): 863–914. doi:10.1103/RevModPhys.51.863. ISSN 0034-6861.
- ^ Friedrich, Bretislav; Herschbach, Dudley (December 2003). "Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics". Physics Today. 56 (12): 53–59. doi:10.1063/1.1650229. ISSN 0031-9228.
- ^ "December 18, 1926: Gilbert Lewis coins "photon" in letter to Nature". www.aps.org. Retrieved 2019-03-09.