User:Johnjbarton/sandbox/introduction to quantum mechanics
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 that cathode rays were actually "corpuscles" or particles now called electrons. Since no solid theory of cathode rays existed, the electron was exciting news, but not a revolution. However, in 1905 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 Young's work on diffraction. Light quanta would be revolutionary.
Einstein's evidence was twofold. First he analyzed blackbody radiation. 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. Einstein showed that, by assuming that light energy transferred in discrete "energy quanta", the radiation curve could be explained. Max Planck showed the same result five years earlier, but he did not propose that the light was quantized.
Einstein's second evidence 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. Then 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 the electron would be accelerated to higher velocity if the light intensity was increased. Einstein's energy quanta explained the increase: one electron is ejected for each quanta: more quanta means 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 Einstein's prediction was completely verified. During that time many scientists rejected the revolutionary idea of quanta.[2] 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 | 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
- ^ Cite error: The named reference
Whittakerwas invoked but never defined (see the help page). - ^ 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.