User:Johnjbarton/sandbox/introduction to quantum mechanics: Difference between revisions

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{{Userspace draft|help=no|date=June 2023|extra=New content for [[Introduction to quantum mechanics]]. '''Status:''' ''adding references, looking for feedback on scope''.}}

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== History ==

{{main | History of quantum mechanics}}

[[History of Maxwell's equations | 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.<ref name="Whittaker">{{Cite book |last=Whittaker |first=Edmund T. |title=A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 |date=1989 |publisher=Dover Publ |isbn=978-0-486-26126-3 |edition=Repr |___location=New York}}</ref>

=== Evidence of quanta from the photoelectric effect ===

{{main | 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 earlier 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]].<ref name=Baggott>{{Cite book |last=Baggott |first=J. E. |title=The quantum story: a history in 40 moments |date=2013 |publisher=Oxford Univ. Press |isbn=978-0-19-965597-7 |edition=Impression: 3 |___location=Oxford}}</ref>

[[File:Black body.svg|thumb|upright=1.4|Blackbody radiation intensity vs color and temperature. The rainbow bar represents visible light; 5000K objects are "white hot" by mixing differing colors of visible light. To the right is the invisible infrared. Classical theory (black curve for 5000K) fails; the other curves are correct predicted by quantum theories.]]

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 predicted by this model.

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.<ref name=Baggott/>{{rp|23}}

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 [[work function | barrier]], the fixed value, that the electrons must climb over to exit their atoms, to be emitted from the metal surface and be measured.

Ten years elapsed before Millikan's definitive experiment<ref>{{Cite journal |last=Millikan |first=R. A. |date=1916-03-01 |title=A Direct Photoelectric Determination of Planck's " h " |url=https://link.aps.org/doi/10.1103/PhysRev.7.355 |journal=Physical Review |language=en |volume=7 |issue=3 |pages=355–388 |doi=10.1103/PhysRev.7.355 |issn=0031-899X}}</ref> verified Einstein's prediction. During that time many scientists rejected the revolutionary idea of quanta.<ref name=pais>{{Cite journal |last=Pais |first=A. |date=1979-10-01 |title=Einstein and the quantum theory |url=https://link.aps.org/doi/10.1103/RevModPhys.51.863 |journal=Reviews of Modern Physics |language=en |volume=51 |issue=4 |pages=863–914 |doi=10.1103/RevModPhys.51.863 |issn=0034-6861}}</ref> But Planck's and Einstein's concept was in the air and soon affected other theories.

=== Quantization of bound electrons in atoms ===

{{main | Atomic theory | Bohr atom | Bohr-Sommerfeld model}}

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.<ref name=Whittaker>{{Cite book |last=Whittaker |first=Edmund T. |title=A history of the theories of aether & electricity. 2: The modern theories, 1900 - 1926 |date=1989 |publisher=Dover Publ |isbn=978-0-486-26126-3 |edition=Repr |___location=New York}}</ref>{{rp|v1:376}} The origin of this regularity was unknown. Solving this mystery would become first major step toward quantum mechanics.

Throughout the 19th century evidence grew for the [[atomic theory|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 [[Plum pudding model|proposed]] negative electrons swimming in a pool of positive charge. Between 1908 and 1911, [[Rutherford model | Rutherford]] showed that the positive part was only 1/3000th of the diameter of the atom.<ref name=baggott/>{{rp|26}}

Models of "planetary" electrons orbiting a nuclear "Sun" were proposed, but cannot explain why the electron does not simply fall into the positive charge. 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.<ref name=baggott/>{{rp|31}}

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 ===

{{main | Matter wave | Schrodinger Equation }}

In 1922 [[Otto Stern]] and [[Walther Gerlach]] [[Stern-Gerlach experiment |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.<ref name="cigar">{{Cite journal |last=Friedrich |first=Bretislav |last2=Herschbach |first2=Dudley |date=December 2003 |title=Stern and Gerlach: How a Bad Cigar Helped Reorient Atomic Physics |url=http://physicstoday.scitation.org/doi/10.1063/1.1650229 |journal=Physics Today |language=en |volume=56 |issue=12 |pages=53–59 |doi=10.1063/1.1650229 |issn=0031-9228}}</ref> Unlike the other then known quantum effects, this striking result involves the state of a single atom.<ref name=Whittaker/>{{rp|v2:130}}

In 1924 [[Louis de Broglie]] proposed<ref name=Broglie>{{cite web |last1=de Broglie |first1=Louis Victor |title=On the Theory of Quanta |url=https://fondationlouisdebroglie.org/LDB-oeuvres/De_Broglie_Kracklauer.pdf |access-date=25 February 2023 |website=Foundation of Louis de Broglie |edition=English translation by A.F. Kracklauer, 2004.}}</ref> 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 [[Schrodinger equation | wave equation]] for electrons; when applied to hydrogen the Rydberg formula was accurately reproduced.<ref name=baggott/>{{rp|65}}

[[Max Born]]'s 1924 paper ''"Zur Quantenmechanik"'' was the first use of the words "quantum mechanics" in print.<ref>Max Born, ''My Life: Recollections of a Nobel Laureate'', Taylor & Francis, London, 1978. ("We became more and more convinced that a radical change of the foundations of physics was necessary, i.e., a new kind of mechanics for which we used the term quantum mechanics. This word appears for the first time in physical literature in a paper of mine...")</ref><ref>{{Cite journal |last=Fedak |first=William A. |last2=Prentis |first2=Jeffrey J. |date=2009-02-01 |title=The 1925 Born and Jordan paper “On quantum mechanics” |url=https://people.isy.liu.se/icg/jalar/kurser/QF/references/onBornJordan1925.pdf |journal=American Journal of Physics |language=en |volume=77 |issue=2 |pages=128–139 |doi=10.1119/1.3009634 |issn=0002-9505}}</ref> His later work included developing quantum collision models; in a footnote to a 1926 paper he proposed the [[Born rule]] connecting theoretical models to experiment.<ref name=Zeitschrift>

{{cite book

|last=Born

|first=Max

|author-link=Max Born

|editor1-last=Wheeler

|editor1-first=J. A.

|editor1-link=John Archibald Wheeler

|editor2-last=Zurek

|editor2-first=W. H.

|editor2-link=Wojciech H. Zurek

|title=Zur Quantenmechanik der Stoßvorgänge

|journal=Zeitschrift für Physik

|volume=37

|issue=12

|trans-title=On the quantum mechanics of collisions

|date=1926

|publisher=Princeton University Press

|publication-date=1983

|doi=10.1007/BF01397477

|isbn=978-0-691-08316-2

|section=I.2

|pages=863–867

|bibcode = 1926ZPhy...37..863B |s2cid=119896026

}}

</ref>

In 1928 [[Paul Dirac]] published his [[Dirac equation | relativistic wave equation]] simultaneously incorporating [[Theory of relativity| relativity]], predicting [[anti-matter]], and providing a complete theory for the Stern-Gerlach result (that there are only two directions that can be measured for silver atoms and for electrons themselves).<ref name=baggott/>{{rp|131}} These successes launched a new fundamental understanding of our world at small scale: 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 ===

{{main | History of quantum field theory}}

In 1923 [[Compton scattering| Compton]] demonstrated that the Planck-Einstein energy quanta from light also had momentum; three years later the "energy quanta" got a new name "[[photon]]"<ref name="photon-named">.{{Cite web|url=https://www.aps.org/publications/apsnews/201212/physicshistory.cfm|title=December 18, 1926: Gilbert Lewis coins "photon" in letter to Nature| website=www.aps.org|language=en|access-date=2019-03-09}}</ref> Despite its role in almost all stages of the quantum revolution, no explicit model for light quanta existed until 1927 when [[Paul Dirac]] began work on a quantum theory of radiation<ref>{{Cite journal |date=1927-03-01 |title=The quantum theory of the emission and absorption of radiation |url=https://royalsocietypublishing.org/doi/10.1098/rspa.1927.0039 |journal=Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character |language=en |volume=114 |issue=767 |pages=243–265 |doi=10.1098/rspa.1927.0039 |issn=0950-1207}}</ref> that became [[quantum electrodynamics]]. Over the following decades this work evolved into [[quantum field theory]], the basis for modern [[quantum optics]] and [[particle physics]].