“God knows I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is[i].” [1]
- Erwin Schrödinger
Maybe Erwin Rudolf Josef Alexander Schrödinger did not care much for probability theory, but he could not avoid it when trying to formulate his wave theory—and the Schrödinger equation—for subatomic particles. Schrödinger (12 August 1887 – 4 January 1961) was a physicist and theoretical biologist who was one of the fathers of quantum mechanics, and is famed for a number of important contributions to physics, especially the Schrödinger equation, for which he received the Nobel Prize in Physics in 1933. In 1935, after extensive correspondence with friend Albert Einstein, he proposed the Schrödinger’s cat thought experiment[ii]. In 1887, Schrödinger was born in Vienna, Austria to Rudolf Schrödinger (cerecloth producer, botanist) and Georgine Emilia Brenda (daughter of Alexander Bauer, Professor of Chemistry, k.u.k. Technische Hochschule Vienna).
His mother was half-Austrian and half English; the English side of her family came from Leamington Spa. Schrödinger learned English and German almost at the same time because both were spoken in the family household. His father was a Catholic and his mother was a Lutheran.
In 1898, he attended the Akademisches Gymnasium. Between 1906 and 1910, Schrödinger studied in Vienna under Franz Serafin Exner[iii] (1849–1926) and Friedrich Hasenöhrl[iv] (1874–1915). He also conducted experimental work with Karl Wilhelm Friedrich (“Fritz”) Kohlrausch (1884–1953) [2]. In 1911, Schrödinger became an assistant to Exner. At an early age, Schrödinger was strongly influenced by Schopenhauer[v] [3]. As a result of his extensive reading of Schopenhauer’s works, he became deeply interested throughout his life in color theory, philosophy[vi], perception, and eastern religion, especially Hindu Vedānta [vii].
Middle years
Middle years
In 1914, Erwin Schrödinger achieved Habilitation[viii] (venia legendi). Between 1914 and 1918, he participated in war work as a commissioned officer in the Austrian fortress artillery (Gorizia, Duino, Sistiana, Prosecco, and Vienna). On 6 April 1920, Schrödinger married Annemarie Bertel. The same year, he became the assistant to Max Wien, in Jena, and in September 1920, he attained the position of ao. Prof. (Ausserordentlicher Professor), roughly equivalent to Reader (UK) or associate professor (US), in Stuttgart. In 1921, he became o. Prof. (Ordentlicher Professor, i.e. full professor), in Breslau (now Wrocław, Poland).
In 1921, he moved to the University of Zürich. In January 1926, Schrödinger published in Annalen der Physik the paper “Quantisierung als Eigenwertproblem” [translation: “Quantization as an Eigenvalue Problem[ix]“] on wave mechanics and what is now known as the Schrödinger equation[x]. In this paper, he gave a “derivation” of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator[xi], the rigid rotor[xii] and the diatomic molecule[xiii], and gives a new derivation of the Schrödinger equation. A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect[xiv]. A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.
In 1927, he succeeded Max Planck at the Friedrich Wilhelm University in Berlin. In 1933, however, Schrödinger decided to leave Germany; he disliked the Nazis‘ anti-Semitism. He became a Fellow of Magdalen College at the University of Oxford. Soon after he arrived, he received the Nobel Prize together with Paul Dirac. His position at Oxford did not work out; his unconventional personal life (Schrödinger lived with two women) [4] was not met with acceptance. In 1934, Schrödinger lectured at Princeton University; he was offered a permanent position there, but did not accept it. Again, his wish to set up house with his wife and his mistress may have posed a problem. He had the prospect of a position at the University of Edinburgh but visa delays occurred, and in the end, he took up a position at the University of Graz in Austria in 1936.
In the midst of these tenure issues in 1935, after extensive correspondence with friend Albert Einstein, he proposed the Schrödinger’s cat thought experiment.
Later years
Later years
In 1939, after the Anschluss[xv], Schrödinger had problems because of his flight from Germany in 1933 and his known opposition to Nazism. He issued a statement recanting this opposition (he later regretted doing so, and he personally apologized to Einstein). However, this did not fully appease the new dispensation and the university dismissed him from his job for political unreliability. He suffered harassment and received instructions not to leave the country, but he and his wife fled to Italy. From there he went to visiting positions in Oxford and Ghent Universities.
In 1940, he received a personal invitation from Ireland’s Taoiseach (prime minister) Éamon de Valera[xvi] to reside in Ireland and agree to help establish an Institute for Advanced Studies in Dublin. He moved to Clontarf, Dublin, became the Director of the School for Theoretical Physics, and remained there for 17 years, during which time he became a naturalized Irish citizen. He wrote about 50 further publications on various topics, including his explorations of unified field theory[xvii].
In 1944, he wrote, “What is Life?” In this book, Schrödinger discusses the limitations of science (physics) in explaining life: “We must therefore not be discouraged by the difficulty of interpreting life by the ordinary laws of physics. For that is just what is to be expected from the knowledge we have gained of the structure of living matter. We must also be prepared to find a new type of physical law prevailing in it. Or are we to term it a non-physical, not to say a super-physical, law?” [5] Though this limitation exists, the book contains a discussion of negentropy[xviii] and the concept of a complex molecule with the genetic code for living organisms. According to James D. Watson’s memoir, DNA, the Secret of Life, Schrödinger’s book gave Watson the inspiration to research the gene, which led to the discovery of the DNA double helix structure. Similarly, Francis Crick, in his autobiographical book What Mad Pursuit, described how he was influenced by Schrödinger’s speculations about how genetic information might be stored in molecules. However, the geneticist and 1946 Nobel-prize winner H. J. Muller had in his 1922 article “Variation due to Change in the Individual Gene” [6] already laid out all the basic properties of the heredity molecule that Schrödinger derives from first principles in What is Life?, properties which Muller refined in his 1929 article “The Gene As The Basis of Life” [7] and further clarified during the 1930s, long before the publication of What is Life? [225].
In Nature and the Greeks (1954), Schrödinger discusses the limitations of the physical world for supplying meaning to every aspect of existence or reality. He writes [8]:
“I am very astonished that the scientific picture of the real world around me is deficient. It gives a lot of factual information, puts all our experience in a magnificently consistent order, but it is ghastly silent about all and sundry that is really near to our heart, that really matters to us. It cannot tell us a word about red and blue, bitter and sweet, physical pain and physical delight; it knows nothing of beautiful and ugly, good or bad, God and eternity. Science sometimes pretends to answer questions in these domains, but the answers are very often so silly that we are not inclined to take them seriously.”
Schrödinger stayed in Dublin until retiring in 1955. During this time he remained committed to his particular passion; involvements with students occurred and he fathered two children by two different Irish women [1] [4]. He had a life-long interest in the Vedānta philosophy of Hinduism, which influenced his speculations at the close of “What is Life?” about the possibility that individual consciousness is only a manifestation of a unitary consciousness pervading the universe [9].
In 1956, he returned to Vienna (chair ad personam). At an important lecture during the World Energy Conference, he refused to speak on nuclear energy because of his skepticism about it and gave a philosophical lecture instead. During this period, Schrödinger turned from mainstream quantum mechanics‘ definition of wave-particle duality and promoted the wave idea alone causing much controversy.
Schrödinger suffered from tuberculosis and several times in the 1920s stayed at a sanatorium in Arosa. It was there that he discovered his wave equation [10].
Schrödinger decided in 1933 that he could not live in a country in which persecution of Jews had become a national policy. Alexander Frederick Lindemann, the head of physics at Oxford University, visited Germany in the spring of 1933 to try to arrange positions in England for some young Jewish scientists from Germany. He spoke to Schrödinger about posts for one of his assistants and was surprised to discover that Schrödinger himself was interested in leaving Germany. Schrödinger asked for a colleague, Arthur March, to be offered a post as his assistant.
The request for March stemmed from Schrödinger’s unconventional relationships with women: although his relations with his wife Anny were good, he had had many lovers with his wife’s full knowledge (and in fact, Anny had her own lover, Hermann Weyl). Schrödinger asked for March to be his assistant because, at that time, he was in love with March’s wife Hilde.
The request for March stemmed from Schrödinger’s unconventional relationships with women: although his relations with his wife Anny were good, he had had many lovers with his wife’s full knowledge (and in fact, Anny had her own lover, Hermann Weyl). Schrödinger asked for March to be his assistant because, at that time, he was in love with March’s wife Hilde.
Many of the scientists who had left Germany spent mid-1933 in the Italian province of South Tyrol. Here Hilde became pregnant with Schrödinger’s child. On 4 November 1933 Schrödinger, his wife and Hilde March arrived in Oxford. Schrödinger had been elected a fellow of Magdalen College. Soon after they arrived in Oxford, Schrödinger heard that, for his work on wave mechanics, he had been awarded the Nobel Prize.
In early 1934, Schrödinger was invited to lecture at Princeton University and while there, he was made an offer of a permanent position. On his return to Oxford, he negotiated about salary and pension conditions at Princeton but in the end, he did not accept. It is thought that the fact that he wished to live at Princeton with Anny and Hilde both sharing the upbringing of his child was not found acceptable. The fact that Schrödinger openly had two wives, even if one of them was married to another man, was not well received in Oxford either. Nevertheless, his daughter Ruth Georgie Erica was born there on 30 May 1934 [1].
On 4 January 1961, Schrödinger died in Vienna at the age of 73 of tuberculosis. He left a widow, Anny (born Annemarie Bertel on 3 December 1896, died 3 October 1965), and was buried in Alpbach, Austria.
The philosophical issues raised by Schrödinger’s cat are still debated today and remains his most enduring legacy in popular science, while Schrödinger’s equation is his most enduring legacy at a more technical level. The huge crater Schrödinger, on the far side of the Moon is named after him. The Erwin Schrödinger International Institute for Mathematical Physics was established in Vienna in 1993.
One of Schrödinger’s lesser-known areas of scientific contribution was his work on color, color perception, and colorimetry[xix] (Farbenmetrik). In 1920, he published three papers in this area:
· “Theorie der Pigmente von größter Leuchtkraft,” Annalen der Physik, (4), 62, (1920), 603-622
· “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Annalen der Physik, (4), 63, (1920), 397-426; 427-456; 481-520 (Outline of a theory of color measurement for daylight vision)
· “Farbenmetrik,” Zeitschrift für Physik, 1, (1920), 459-466 (Color measurement).
The second of these is available in English as “Outline of a Theory of Color Measurement for Daylight Vision” in Sources of Color Science, Ed. David L. MacAdam, The MIT Press (1970), 134-182.
· “Grundlinien einer Theorie der Farbenmetrik im Tagessehen,” Annalen der Physik, (4), 63, (1920), 397-426; 427-456; 481-520 (Outline of a theory of color measurement for daylight vision)
· “Farbenmetrik,” Zeitschrift für Physik, 1, (1920), 459-466 (Color measurement).
The second of these is available in English as “Outline of a Theory of Color Measurement for Daylight Vision” in Sources of Color Science, Ed. David L. MacAdam, The MIT Press (1970), 134-182.
Works Cited
[1] Moore, Walter J., Schrödinger: Life and Thought. s.l. : Cambridge University Press, 1992. p. 222. ISBN-13: 978-0521437677 .
[2] Nobelprize.org., Erwin Schrödinger - Biography. The Nobel Prize in Physics 1933. [Online] The Nobel Foundation, 1933. [Cited: July 20, 2011.] http://nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html.
[3] Moore, Walter J., A Life of Erwin Schrödinger. Abridged edition. s.l. : Cambridge University Press, 1994. ISBN-13: 978-0521469340.
[4] O'Connor, J. J. and Robertson, E. F., Erwin Rudolf Josef Alexander Schrödinger. School of Mathematics and Statistics, University of St Andrews, Scotland . 2003. http://www-history.mcs.st-andrews.ac.uk/Biographies/Schrodinger.html. Retrieved 20 July 2011..
[5] Schrödinger, Erwin., What is Life?: with "Mind and Matter" and "Autobiographical Sketches". s.l. : Cambridge University Press, 1992. ISBN-13: 978-0521427081.
[6] Meÿenn, Karl., "Schrödinger, Erwin Rudolf Josef Alexander." Neue Deutsche Biographie. online version, 2007, Vol. 23, pp. 578-580. http://www.deutsche-biographie.de/pnd118823574.html.
[7] Muller, H. J., The American Naturalist: V.56 1922. s.l. : University of Michigan Library, 2001 [1929]. ASIN: B002IKLF18 .
[8] Schrödinger, Erwin., 'Nature and the Greeks' and 'Science and Humanism'. s.l. : Cambridge University Press, 1996. ISBN-13: 978-0521575508.
[9] Schwartz, James., In Pursuit of the Gene. From Darwin to DNA. s.l. : Harvard University Press, 2008. ISBN-13: 978-0674026704.
[10] New World Encyclopedia., "Schrödinger, Erwin." New World Encyclopedia. April 24, 2008. http://www.newworldencyclopedia.org/entry/Erwin_Schr%C3%B6dinger.
[2] Nobelprize.org., Erwin Schrödinger - Biography. The Nobel Prize in Physics 1933. [Online] The Nobel Foundation, 1933. [Cited: July 20, 2011.] http://nobelprize.org/nobel_prizes/physics/laureates/1933/schrodinger-bio.html.
[3] Moore, Walter J., A Life of Erwin Schrödinger. Abridged edition. s.l. : Cambridge University Press, 1994. ISBN-13: 978-0521469340.
[4] O'Connor, J. J. and Robertson, E. F., Erwin Rudolf Josef Alexander Schrödinger. School of Mathematics and Statistics, University of St Andrews, Scotland . 2003. http://www-history.mcs.st-andrews.ac.uk/Biographies/Schrodinger.html. Retrieved 20 July 2011..
[5] Schrödinger, Erwin., What is Life?: with "Mind and Matter" and "Autobiographical Sketches". s.l. : Cambridge University Press, 1992. ISBN-13: 978-0521427081.
[6] Meÿenn, Karl., "Schrödinger, Erwin Rudolf Josef Alexander." Neue Deutsche Biographie. online version, 2007, Vol. 23, pp. 578-580. http://www.deutsche-biographie.de/pnd118823574.html.
[7] Muller, H. J., The American Naturalist: V.56 1922. s.l. : University of Michigan Library, 2001 [1929]. ASIN: B002IKLF18 .
[8] Schrödinger, Erwin., 'Nature and the Greeks' and 'Science and Humanism'. s.l. : Cambridge University Press, 1996. ISBN-13: 978-0521575508.
[9] Schwartz, James., In Pursuit of the Gene. From Darwin to DNA. s.l. : Harvard University Press, 2008. ISBN-13: 978-0674026704.
[10] New World Encyclopedia., "Schrödinger, Erwin." New World Encyclopedia. April 24, 2008. http://www.newworldencyclopedia.org/entry/Erwin_Schr%C3%B6dinger.
Notes
[i] 13th of June, 1946, in a letter to Albert Einstein, as quoted by Walter Moore in Schrödinger: Life and Thought (1989) ISBN 0521437679
[ii] Schrödinger’s cat is a thought experiment (see Chapter 37), usually described as a paradox, that Austrian physicist Erwin Schrödinger devised in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung (entanglement).
[iii] Franz Serafin Exner (24 March 1849 - October 15, 1926) was an Austrian physicist.
[iv] Friedrich Hasenöhrl (November 30, 1874 - October 7, 1915) was an Austro-Hungarian physicist.
[v] Arthur Schopenhauer (22 February 1788 – 21 September 1860) was a German philosopher known for his pessimism and philosophical clarity.
[vi] In his lecture "Mind and Matter," Chapter 4, he said that a phrase "that has become familiar to us" is "The world extended in space and time is but our representation (Vorstellung)." This is a repetition of the first words of Schopenhauer’s main work.
[vii] Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads.
[viii] Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a Ph.D., habilitation requires the candidate to write a professorial thesis (often known as a Habilitationsschrift, or Habilitation thesis) based on independent scholarship, reviewed by and defended before an academic committee in a process similar to that for the doctoral dissertation. However, the level of scholarship has to be considerably higher than that required for a research doctoral (Ph.D.) thesis in terms of quality and quantity, and must be accomplished independently, in contrast with a Ph.D. dissertation typically directed or guided by a faculty supervisor.
[ix] The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain proportional to the original vector (i.e., change only in magnitude, not in direction). For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector changes when multiplied by the matrix. The prefix eigen- is adopted from the German word "eigen" for "own" in the sense of a characteristic description. The eigenvectors are sometimes also called characteristic vectors. Similarly, the eigenvalues are also known as characteristic values.
[x] The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics, specifically quantum mechanics, it is an equation that describes how the quantum state of a physical system changes in time. In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger’s equation describe not only molecular, atomic and subatomic systems, but also macroscopic systems, possibly even the whole universe.
[xi] The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which a simple, exact solution is known.
[xii] The rigid rotor is a mechanical model that is used to explain rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space three angles are required. A special rigid rotor is the linear rotor that is a 2-dimensional object, requiring two angles to describe its orientation. An example of a linear rotor is a diatomic molecule. More general molecules like water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor) are 3-dimensional, see classification of molecules.
[xiii] Diatomic molecules are molecules composed only of two atoms, of either the same or the different chemical elements. The prefix di- means two in Greek. Common diatomic molecules are hydrogen (H2), nitrogen (N2), oxygen (O2), and carbon monoxide (CO). Seven elements exist in the diatomic state in the liquid and solid forms: H2 , N2, O2, F2, Cl2, Br2, and I2. Most elements (and many chemical compounds) aside from these form diatomic molecules when evaporated, although at very high temperatures, all materials disintegrate into atoms. The noble gases do not form diatomic molecules.
[xiv] The Stark effect (named after Johannes Starck)is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift.
[xv] The Anschluss (spelled Anschluß at the time of the event, and until the German orthography reform of 1996; German for "link-up"), also known as the Anschluss Österreichs, was the occupation and annexation of Austria into Nazi Germany in 1938.
[xvi] Éamon de Valera(14 October 1882 – 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government and head of state and introducing the Constitution of Ireland. De Valera was a leader of Ireland’s struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
[xvii] Since the 19th century, some physicists have attempted to develop a single theoretical framework that can account for the fundamental forces of nature—a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between World War I and World War II. This work spurred the purely mathematical development of differential geometry. Albert Einstein is the best known of the many physicists who attempted to develop a classical unified field theory.
[xviii] The negentropy, also negative entropy or syntropy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life. The concept and phrase "negative entropy" were introduced by Erwin Schrödinger in his 1943 popular-science book What is Life?
[xix] Colorimetry is "the science and technology used to quantify and describe physically the human color perception."
[ii] Schrödinger’s cat is a thought experiment (see Chapter 37), usually described as a paradox, that Austrian physicist Erwin Schrödinger devised in 1935. It illustrates what he saw as the problem of the Copenhagen interpretation of quantum mechanics applied to everyday objects. The thought experiment presents a cat that might be alive or dead, depending on an earlier random event. In the course of developing this experiment, he coined the term Verschränkung (entanglement).
[iii] Franz Serafin Exner (24 March 1849 - October 15, 1926) was an Austrian physicist.
[iv] Friedrich Hasenöhrl (November 30, 1874 - October 7, 1915) was an Austro-Hungarian physicist.
[v] Arthur Schopenhauer (22 February 1788 – 21 September 1860) was a German philosopher known for his pessimism and philosophical clarity.
[vi] In his lecture "Mind and Matter," Chapter 4, he said that a phrase "that has become familiar to us" is "The world extended in space and time is but our representation (Vorstellung)." This is a repetition of the first words of Schopenhauer’s main work.
[vii] Vedānta was originally a word used in Hindu philosophy as a synonym for that part of the Veda texts known also as the Upanishads.
[viii] Habilitation is the highest academic qualification a scholar can achieve by his or her own pursuit in several European and Asian countries. Earned after obtaining a research doctorate, such as a Ph.D., habilitation requires the candidate to write a professorial thesis (often known as a Habilitationsschrift, or Habilitation thesis) based on independent scholarship, reviewed by and defended before an academic committee in a process similar to that for the doctoral dissertation. However, the level of scholarship has to be considerably higher than that required for a research doctoral (Ph.D.) thesis in terms of quality and quantity, and must be accomplished independently, in contrast with a Ph.D. dissertation typically directed or guided by a faculty supervisor.
[ix] The eigenvectors of a square matrix are the non-zero vectors that, after being multiplied by the matrix, remain proportional to the original vector (i.e., change only in magnitude, not in direction). For each eigenvector, the corresponding eigenvalue is the factor by which the eigenvector changes when multiplied by the matrix. The prefix eigen- is adopted from the German word "eigen" for "own" in the sense of a characteristic description. The eigenvectors are sometimes also called characteristic vectors. Similarly, the eigenvalues are also known as characteristic values.
[x] The Schrödinger equation was formulated in 1926 by Austrian physicist Erwin Schrödinger. Used in physics, specifically quantum mechanics, it is an equation that describes how the quantum state of a physical system changes in time. In the standard interpretation of quantum mechanics, the quantum state, also called a wavefunction or state vector, is the most complete description that can be given to a physical system. Solutions to Schrödinger’s equation describe not only molecular, atomic and subatomic systems, but also macroscopic systems, possibly even the whole universe.
[xi] The quantum harmonic oscillator is the quantum-mechanical analog of the classical harmonic oscillator. Because an arbitrary potential can be approximated as a harmonic potential at the vicinity of a stable equilibrium point, it is one of the most important model systems in quantum mechanics. Furthermore, it is one of the few quantum-mechanical systems for which a simple, exact solution is known.
[xii] The rigid rotor is a mechanical model that is used to explain rotating systems. An arbitrary rigid rotor is a 3-dimensional rigid object, such as a top. To orient such an object in space three angles are required. A special rigid rotor is the linear rotor that is a 2-dimensional object, requiring two angles to describe its orientation. An example of a linear rotor is a diatomic molecule. More general molecules like water (asymmetric rotor), ammonia (symmetric rotor), or methane (spherical rotor) are 3-dimensional, see classification of molecules.
[xiii] Diatomic molecules are molecules composed only of two atoms, of either the same or the different chemical elements. The prefix di- means two in Greek. Common diatomic molecules are hydrogen (H2), nitrogen (N2), oxygen (O2), and carbon monoxide (CO). Seven elements exist in the diatomic state in the liquid and solid forms: H2 , N2, O2, F2, Cl2, Br2, and I2. Most elements (and many chemical compounds) aside from these form diatomic molecules when evaporated, although at very high temperatures, all materials disintegrate into atoms. The noble gases do not form diatomic molecules.
[xiv] The Stark effect (named after Johannes Starck)is the shifting and splitting of spectral lines of atoms and molecules due to the presence of an external static electric field. The amount of splitting and or shifting is called the Stark splitting or Stark shift.
[xv] The Anschluss (spelled Anschluß at the time of the event, and until the German orthography reform of 1996; German for "link-up"), also known as the Anschluss Österreichs, was the occupation and annexation of Austria into Nazi Germany in 1938.
[xvi] Éamon de Valera(14 October 1882 – 29 August 1975) was one of the dominant political figures in twentieth century Ireland, serving as head of government and head of state and introducing the Constitution of Ireland. De Valera was a leader of Ireland’s struggle for independence from Britain in the Irish War of Independence and of the anti-Treaty forces in the ensuing Irish Civil War (1922–23). In 1926, he founded Fianna Fáil and was head of government from 1932–48, 1951–54 and 1957–59 and President of Ireland from 1959–73.
[xvii] Since the 19th century, some physicists have attempted to develop a single theoretical framework that can account for the fundamental forces of nature—a unified field theory. Classical unified field theories are attempts to create a unified field theory based on classical physics. In particular, unification of gravitation and electromagnetism was actively pursued by several physicists and mathematicians in the years between World War I and World War II. This work spurred the purely mathematical development of differential geometry. Albert Einstein is the best known of the many physicists who attempted to develop a classical unified field theory.
[xviii] The negentropy, also negative entropy or syntropy, of a living system is the entropy that it exports to keep its own entropy low; it lies at the intersection of entropy and life. The concept and phrase "negative entropy" were introduced by Erwin Schrödinger in his 1943 popular-science book What is Life?
[xix] Colorimetry is "the science and technology used to quantify and describe physically the human color perception."
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