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003389c870a2ea4ff3b3fbd3e257d6dac39e0e8a | a hydrogen atom consists of an electron orbiting | a hydrogen atom consists of an electron orbiting its nucleus. the electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. these states were visualized by the bohr model of the hydrogen atom as being distinct orbits around the nucleus... | wikipedia |
1fda3d707545243134d0eb41974feac25e27c604 | the emission spectrum of atomic hydrogen has been | the emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the rydberg formula. these observed spectral lines are due to the electron making transitions between two energy levels in an atom. the classification of the series by the rydberg formula was important ... | wikipedia |
8d7475a9e8b3093b59d170c1c7edf2eb0048815c | ynés enriquetta julietta mexía was a mexican-american botanist | ynés enriquetta julietta mexía was a mexican-american botanist notable for her extensive collection of novel specimens of flora and plants originating from sites in colombia, mexico, and peru. she discovered a new genus of asteraceae, known after her as mexianthus, and accumulated over 150,000 specimens for botanical s... | wikipedia |
c11f20e4aa88ece28b310e12e9a5403f397f6543 | a large portion of her estate was left | a large portion of her estate was left to the sierra club and the save the redwoods league to further environmental conservation. mexía provided funding for vernon orlando bailey to create and produce his pioneering invention of more humane traps for animals. | wikipedia |
9bead0f63c40bc067c7f4e6fa52033b074df6a7d | other researchers benefited from her knowledge of central | other researchers benefited from her knowledge of central and south american culture and natural environment and her fluency with the spanish language. thomas harper goodspeed, botanist and former director of the university of california botanical garden, travelled with mexía to the andes mountains, and commented that ... | wikipedia |
a4c42897640fa1017de049b2c92540eb4a65e1e3 | mexía is remembered by her colleagues for her | mexía is remembered by her colleagues for her expertise in fieldwork, resilience in the face of difficult and dangerous conditions, as well as her impulsiveness and fractious but generous personality. she was known and praised for her meticulous, exacting work and her skills as a botanical collector. | wikipedia |
251f9a1cb5550b3bdcce6180cc7ebc8a3336b63b | though mexía had a short professional career—only 13 | though mexía had a short professional career—only 13 years—compared to many other academics, she collected a huge number of plant specimens. according to the british natural history museum, she collected at least 145,000 plant specimens during her travels, 500 of which were new species (mostly spermatophytes). there ha... | wikipedia |
40a139ec60046d34de9d0a9f9f721c57efed7db1 | "women were actively dissuaded from doing that kind | "women were actively dissuaded from doing that kind of work, because it was considered unfeminine and dangerous," says. "you actually have to camp out, you couldn’t wash your hair, you were living a kind of rough life, and that could be dangerous…. but mexía had agency. she was doing exactly the work that she wanted to... | wikipedia |
eb508fff8997e3223281133aafb545d0fd2efd4e | mexía was atypical for a botanist or botanical | mexía was atypical for a botanist or botanical collector of her era, as a woman, a person of mexican heritage under-represented in her field, and an older person who had begun her career in her mid-fifties. vassiliki betty smocovitis, a professor of the history of science at the university of florida, explains that: | wikipedia |
f56bc9ffd36d9766ebcdf66386edf90be54b7b4c | mexía was an active member of many scientific | mexía was an active member of many scientific societies, including the california botanical society which she joined in 1915, the sierra club, the audubon association of the pacific, the sociedad geográfica de lima, and the california academy of sciences. she was also an honorary member of the departamento forestal, de... | wikipedia |
9b8af9ed244145165989edbfd20d07c637ab2552 | documentation of her expeditions appeared regularly in the | documentation of her expeditions appeared regularly in the gull, the newsletter of the audubon society of the pacific, from 1926 to 1935. the sierra club bulletin archived 2019-02-26 at the wayback machine published two accounts of her travels: "three thousand miles up the amazon" (scb, 18:1, 88–96), and "camping on th... | wikipedia |
06e190b1b75eaea246e1f48354e893171f571366 | in personal correspondence from 1980, the botanist john | in personal correspondence from 1980, the botanist john thomas howell refers to mexía as a "close friend of alice eastwood." he relates that "in 1933 she accompanied miss eastwood and me on the first eastwood and howell collecting expedition.….in an open model t ford, that traversed parts of nevada, utah, arizona, and ... | wikipedia |
7bd52327a44c79531d388c14b948c0700cd3f3fd | in 1928 she was hired to collect plants | in 1928 she was hired to collect plants in mount mckinley national park in alaska, which yielded 6100 specimens. the next year she went to south america and travelled by canoe down the amazon river, covering 4,800 kilometers in two and a half years, ending at its source in the andes. this expedition resulted in 65,000 ... | wikipedia |
6098bc34a46579098994ada1e34d79e888a74fd1 | mexía began her career in botany in 1922 | mexía began her career in botany in 1922 when she joined an expedition led by mr. e. l. furlong, the curator of paleontology at university of california, berkeley. her successes started to mount in 1925 with a two-month excursion to western mexico under the auspices of roxanna ferris, a botanist at stanford university.... | wikipedia |
c13ec2db4399be6f7fb7235d82bc406542599638 | in 1938, while on an expedition to oaxaca, | in 1938, while on an expedition to oaxaca, mexico, mexía became ill. forced to abort the trip and return to the united states, she was subsequently diagnosed with lung cancer and died a month later at the age of 68. william e. colby, then secretary of the sierra club, wrote "all who knew ynés mexía could not fail to be... | wikipedia |
a3a8410e291f18c0e37e93a1a8655207717ef661 | over the course of the next 13 years, | over the course of the next 13 years, mexía traveled from the northern regions of alaska to the southern tip of tierra del fuego. her habits often surprised people she met because she was not acting in a manner typical of a woman of the early 20th century: traveling alone, riding horseback, wearing trousers (knickers),... | wikipedia |
8da3da0a10b8758351badab567d0ed826f31562f | ynés enrolled at university california berkeley, where she | ynés enrolled at university california berkeley, where she was introduced to botany and went on her first expedition. ynés wrote to alice eastwood in july 1925, advising eastwood that she was about to accompany stanford's assistant herbarium curator, roxanna ferris, on a collecting trip to mexico, which would be her fi... | wikipedia |
2194b7dcbf876cd27fae9504c08a212b91d53b6d | in 1909, at the age of 39, mexía | in 1909, at the age of 39, mexía suffered a mental and physical breakdown and left mexico for san francisco in search of medical care. she was treated by dr. philip king brown, founder of the arequipa sanatorium in fairfax, for a total of ten years. while in northern california, mexía began going on excursions with the... | wikipedia |
24c467a676792eb7a5d47abb82ecb00230133c91 | while residing there in 1897, mexia married her | while residing there in 1897, mexia married her first husband, herman de laue, a spanish-german merchant, who died in 1904. around the time of his death, mexia started quinta, a pet and poultry stock raising business, at the hacienda she inherited from her father's estate. later, she married d. augustin reygados, but t... | wikipedia |
f66dbf718b6a9e92a51c19612cc2b7367d7b0256 | in 1873, her father returned to mexico, and | in 1873, her father returned to mexico, and her mother moved ynés and her six half-siblings to a ranch in limestone, texas, later to be called mexia. later, the family moved around in various eastern cities such as philadelphia and ontario, where she received a private school education. they settled in maryland, where ... | wikipedia |
a5f512974aecdda14cc03f60db2cd65065bcf247 | ynés mexía was born on may 24, 1870, | ynés mexía was born on may 24, 1870, in washington d.c. to enrique mexia, a mexican diplomat, and sarah wilmer mexía. her grandfather was josé antonio mexía, a distinguished mexican general. sarah wilmer was related to samuel eccleston, the fifth catholic archbishop of baltimore. | wikipedia |
a838ed99194f1a59315f6e27550dfab9fba20f72 | ynés enriquetta julietta mexía (may 24 1870 – | ynés enriquetta julietta mexía (may 24 1870 – july 12 1938) was a mexican-american botanist notable for her extensive collection of novel specimens of flora and plants originating from sites in colombia, mexico, and peru. she discovered a new genus of asteraceae, known after her as mexianthus, and accumulated over 150,... | wikipedia |
3613fdb7042df6519a08784ef50a2a0c3a2f3064 | robert bartlett is an american physician and medical | robert bartlett is an american physician and medical researcher who is credited with developing a lifesaving heart-lung technology known as extracorporeal membrane oxygenation (ecmo). he is an emeritus professor of surgery at the university of michigan medical school. | wikipedia |
a3660383605908e8cba21930ba861a2b21c9e53f | in 2003, bartlett was awarded the william e. | in 2003, bartlett was awarded the william e. ladd medal by the american academy of pediatrics. the organization says that the medal "represents the highest honor that the section on surgery bestows on a physician in recognition of outstanding contributions to the field of pediatric surgery." he was awarded the medallio... | wikipedia |
5fe2f6b0cf733517e9e3b070e42ab4d1352af40e | bartlett's research has been continuously funded by nih | bartlett's research has been continuously funded by nih since 1971. in addition to ecmo he made major contributions to critical care physiology, acute kidney injury and continuous hemofiltration, and nutrition in critical illness. he has been president of the american society of artificial internal organs and the inter... | wikipedia |
8a84da469aeb912bda16460dba952604033deef0 | bartlett began to write fiction late in his | bartlett began to write fiction late in his medical career. he became interested in writing stories about medicine and the law after testifying as an expert on burns in the appeal of a man's conviction for child abuse. though bartlett was convinced that the defendant was innocent, the man's conviction was not overturne... | wikipedia |
d80d96b13f43e10647db65eb6c077c47baacb022 | in 1980, bartlett came back to the university | in 1980, bartlett came back to the university of michigan and joined the faculty. he spent 25 years as the director of michigan's surgical intensive care unit. he held positions as chief of general surgery, program director of the surgical critical care fellowship, and director of the extracorporeal life support labora... | wikipedia |
6515725c246dc33c46ea613f9147cd2ff388f326 | bartlett reported the first neonatal survivor of ecmo, | bartlett reported the first neonatal survivor of ecmo, referred to as baby esperanza, in 1976. baby esperanza suffered lung damage from meconium aspiration syndrome and she was so sick that ecmo was applied as a last-ditch effort to save her life. the baby spent three days on bartlett's machine and she recovered. | wikipedia |
af7b4d4e32a0e08529a30582975bc72ebeb2ec3a | bartlett spent ten years on the faculty of | bartlett spent ten years on the faculty of the university of california, irvine school of medicine. through laboratory research that began in the 1960s, bartlett helped to develop ecmo technology for babies with potentially reversible heart or lung dysfunction. | wikipedia |
1bde61e68a0d3bf46db65411c91f33b99907fcad | robert bartlett (born may 8, 1939) is an | robert bartlett (born may 8, 1939) is an american physician and medical researcher who is credited with developing a lifesaving heart-lung technology known as extracorporeal membrane oxygenation (ecmo). he is an emeritus professor of surgery at the university of michigan medical school. | wikipedia |
e2c798ce35f4ddb0355606ab641356e750b5a739 | huddersfield viaduct is a railway bridge to the | huddersfield viaduct is a railway bridge to the north-east of huddersfield railway station in west yorkshire, england. the viaduct carries the huddersfield line connecting huddersfield with dewsbury, leeds, and york eastwards, and manchester and liverpool westwards. the viaduct was built to carry two lines, but was wid... | wikipedia |
d6576d096241d830bb58c92e15c92653fe61943e | the viaduct had a new bridge deck built | the viaduct had a new bridge deck built upon it during an engineering blockade over the easter bank holiday weekend of 2024, in preparation for the lines on the viaduct being expanded from two lines to four as part of the trans-pennine route upgrade (tru). other works on the viaduct as part of the tru will include exte... | wikipedia |
6dff2a4dc8b6f53900424369551dd7531ed1ba4c | the viaduct also had a signal box (huddersfield | the viaduct also had a signal box (huddersfield no. 2 signal box), which was about 100 yards (91 m) east of the station. the viaduct crosses over several roads, the huddersfield ring road, the a641 bradford road, and numerous minor roads, but also historically bridged several tram lines and the level road-running indus... | wikipedia |
da9b3a23086622e609e7497116c056353f8e031f | initially the west end of the viaduct (that | initially the west end of the viaduct (that nearest the railway station) had two lines, which widened to accommodate four lines. however, in 1883, the entire structure was widened to take five lines between huddersfield and the yards and depot at hillhouse, using stone which had been quarried from springwood cutting (w... | wikipedia |
d8dd9287e49e1c81ba740e288ba79fa4a40fe9da | the viaduct was opened up to traffic in | the viaduct was opened up to traffic in august 1847 with only a single line connecting huddersfield with heaton lodge junction on the manchester and leeds line through the calder valley. construction of the viaduct started in 1845, but it was delayed in opening as it had to be re-profiled due to there being some error ... | wikipedia |
19b768bc8d9d835ec09c350772aee4885191b2e5 | the first railway in the area was the | the first railway in the area was the manchester and leeds railway (m&l) which passed huddersfield 3.25 miles (5.23 km) to the north. initially, the operators of that line were reluctant to provide a route into huddersfield from the north, but in the face of opposing railway companies submitting bills through parliamen... | wikipedia |
dce9c19c35d646c19f7d0f6ce56028289497921d | as part of the transpennine route upgrade (tru), | as part of the transpennine route upgrade (tru), the viaduct will again have four lines along the whole 663 yards (606 m), and will additionally be electrified with a 25 kv overhead catenary by the 2030s. | wikipedia |
cee7bd27d26c839c0072d817dd7fba15150c7451 | huddersfield viaduct (or hillhouse viaduct) is a railway | huddersfield viaduct (or hillhouse viaduct) is a railway bridge to the north-east of huddersfield railway station in west yorkshire, england. the viaduct carries the huddersfield line connecting huddersfield with dewsbury, leeds, and york eastwards, and manchester and liverpool westwards. the viaduct was built to carry... | wikipedia |
34cb43a955904a9fc5cdb20c9f7317aa6f3b1b40 | sawaya initially started out as a forward and | sawaya initially started out as a forward and winger during his youth career; he later developed into a right-back. he has been likened to former lebanese international ali hamam. sawaya stated that he drew inspiration from former german international philipp lahm. | wikipedia |
fc79151ee7c781cde2780c8ad0d035a4b89492d7 | sawaya represented lebanon internationally at youth level, and | sawaya represented lebanon internationally at youth level, and was called up to the senior team 's training camp ahead of the 2022 fifa world cup qualifiers. he made his senior debut on 30 december 2022, in a 1–0 friendly defeat to the united arab emirates. | wikipedia |
827f1b308b51c9caad965953c5229ce83db99b62 | in july 2017, sawaya joined nejmeh, initially playing | in july 2017, sawaya joined nejmeh, initially playing for both the youth and senior teams. he made one appearance in the 2017–18 lebanese premier league, on 15 april 2018, as a starter in a 3–1 defeat to ahed. sawaya scored against cross-city rivals ansar in the 2021–22 league season, to help nejmeh win 1–0. | wikipedia |
c7eb6b13086822eb8e554bf1dc976548b3eadd15 | born in dhour el choueir, lebanon, sawaya moved | born in dhour el choueir, lebanon, sawaya moved to the united arab emirates aged five, where he lived for seven years. during this time, he played for the academy of al ain. in 2012, he moved back to lebanon, playing for the athletico football academy for five years. | wikipedia |
ab6c7ee85afcbbec471500e4f7e81fc937bcd249 | andrew kameel sawaya (arabic: أندرو كميل صوايا; born | andrew kameel sawaya (arabic: أندرو كميل صوايا; born 30 april 2000) is a lebanese footballer who plays as a right-back for lebanese premier league club safa. | wikipedia |
a3de6a2b278ae5e8d150d97f1fdbc6a2ad2ca8f7 | if a theatrical production won the tony award | if a theatrical production won the tony award for best play, tony award for best musical, tony award for best revival of a play, tony award for best revival of a musical or the tony award for best revival its entry is listed in a shaded background with a boldface title. | wikipedia |
1092764cf4ba95d60b8af6da53017168947f854c | carl wilhelm wolfgang ostwald was a german chemist | carl wilhelm wolfgang ostwald was a german chemist and biologist researching colloids. ostwald was born in riga, the son of the 1909 winner of the nobel prize in chemistry, wilhelm ostwald, and died in dresden. | wikipedia |
de78a040e0d79976d7265ac43502d7544d631012 | in quantum mechanics, the canonical commutation relation is | in quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities. for example, [ x ^ , p ^ x ] = i ℏ i between the position operator x and momentum operator px in the x direction of a point particle in one dimension, where [x, px] = x px − px x is the commutato... | wikipedia |
e57131419fdb65141f354247c70563c9302f8a35 | consequently, the above inequality applied to this commutation | consequently, the above inequality applied to this commutation relation specifies Δ l x Δ l y ≥ 1 2 ℏ 2 | ⟨ l z ⟩ | 2 , {\displaystyle \delta l_{x}\delta l_{y}\geq {\frac {1}{2}}{\sqrt {\hbar ^{2}|\langle l_{z}\rangle |^{2}}}~,} hence | ⟨ l x 2 ⟩ ⟨ l y 2 ⟩ | ≥ ℏ 2 2 | m | {\displaystyle {\sqrt {|\langle l_{x}^{2}\rangl... | wikipedia |
57072b91bb41d451a156d8baf558103127668327 | for the angular momentum operators l = y | for the angular momentum operators l = y p − z p, etc., one has that = i ℏ ϵ x y z l z, {\displaystyle =i\hbar \epsilon _{xyz}{l_{z}},} where ϵ x y z {\displaystyle \epsilon _{xyz}} is the levi-civita symbol and simply reverses the sign of the answer under pairwise interchange of the indices. an analogous relation hold... | wikipedia |
6225cf252fdadeee920df1056b2c0081079c10c2 | this follows through use of the cauchy–schwarz inequality, | this follows through use of the cauchy–schwarz inequality, since | ⟨ a ⟩ | | ⟨ b ⟩ | ≥ | ⟨ a b ⟩ |, and a b = (+ { a, b })/2 ; and similarly for the shifted operators a − ⟨ a ⟩ and b − ⟨ b ⟩. (cf. uncertainty principle derivations.) | wikipedia |
df352b6026543ab849be7addc7049e12ce6e7a38 | then Δ a Δ b ≥ 1 2 | then Δ a Δ b ≥ 1 2 | ⟨ ⟩ | 2 + | ⟨ { a − ⟨ a ⟩, b − ⟨ b ⟩ } ⟩ | 2, {\displaystyle \delta a\,\delta b\geq {\frac {1}{2}}{\sqrt {\left|\left\langle \left\right\rangle \right|^{2}+\left|\left\langle \left\{a-\langle a\rangle,b-\langle b\rangle \right\}\right\rangle \right|^{2}}},} where ≡ a b − b a is the commutator of a ... | wikipedia |
9453ee1c7419b468da06317c5879633311b7dc8b | all such nontrivial commutation relations for pairs of | all such nontrivial commutation relations for pairs of operators lead to corresponding uncertainty relations, involving positive semi-definite expectation contributions by their respective commutators and anticommutators. in general, for two hermitian operators a and b, consider expectation values in a system in the st... | wikipedia |
014dc7df0a6e439f3347ce0d978e82adc14627c9 | the gauge-invariant angular momentum (or "kinetic angular momentum") | the gauge-invariant angular momentum (or "kinetic angular momentum") is given by k = r × (p − q a c), {\displaystyle k=r\times \left(p-{\frac {qa}{c}}\right),} which has the commutation relations = i ℏ ϵ i j k (k k + q ℏ c x k (x ⋅ b)) {\displaystyle =i\hbar {\epsilon _{ij}}^{\,k}\left(k_{k}+{\frac {q\hbar }{c}}x_{k}\l... | wikipedia |
5db09fd212cac3ed2a41ac680d2227032ac7ca96 | the angular momentum operator is l = r | the angular momentum operator is l = r × p {\displaystyle l=r\times p\,\!} and obeys the canonical quantization relations = i ℏ ϵ i j k l k {\displaystyle =i\hbar {\epsilon _{ijk}}l_{k}} defining the lie algebra for so(3), where ϵ i j k {\displaystyle \epsilon _{ijk}} is the levi-civita symbol. under gauge transformati... | wikipedia |
80e9a1ad7744b98c6435b851c37baad3cc3d8352 | the non-relativistic hamiltonian for a quantized charged particle | the non-relativistic hamiltonian for a quantized charged particle of mass m in a classical electromagnetic field is (in cgs units) h = 1 2 m (p − q a c) 2 + q ϕ {\displaystyle h={\frac {1}{2m}}\left(p-{\frac {qa}{c}}\right)^{2}+q\phi } where a is the three-vector potential and φ is the scalar potential. this form of th... | wikipedia |
b2a836803b7562c371ad7bdd01a7155e337be0a2 | where q is the particle's electric charge, a | where q is the particle's electric charge, a is the vector potential, and c is the speed of light. although the quantity p is the "physical momentum", in that it is the quantity to be identified with momentum in laboratory experiments, it does not satisfy the canonical commutation relations; only the canonical momentum... | wikipedia |
6b4117c2eddd43f09c5ea3f4567d6df897eba7c3 | using c n + 1 k = c | using c n + 1 k = c n k + c n k − 1 {\displaystyle c_{n+1}^{k}=c_{n}^{k}+c_{n}^{k-1}}, it can be shown that by mathematical induction = ∑ k = 1 min (m, n) − (− i ℏ) k n ! m ! k ! (n − k) ! (m − k) ! x ^ n − k p ^ m − k = ∑ k = 1 min (m, n) (i ℏ) k n ! m ! k ! (n − k) ! (m − k) ! p ^ m − k x ^ n − k, {\displaystyle \lef... | wikipedia |
354630cb5b6e4a5aea1cf13f3cee871950fec2f8 | further, it can be shown that = i | further, it can be shown that = i ℏ ∂ f (x →) ∂ x i; = i ℏ ∂ f (p →) ∂ p i. {\displaystyle =i\hbar {\frac {\partial f({\vec {x}})}{\partial x_{i}}};\qquad =i\hbar {\frac {\partial f({\vec {p}})}{\partial p_{i}}}.} | wikipedia |
f3ab7eb7189d0eb3096ffd752ec92742f168c74a | this definition of the canonical momentum ensures that | this definition of the canonical momentum ensures that one of the euler–lagrange equations has the form ∂ ∂ t π i = ∂ l ∂ x i. {\displaystyle {\frac {\partial }{\partial t}}\pi _{i}={\frac {\partial {\mathcal {l}}}{\partial x_{i}}}.} | wikipedia |
9d42d904deca11c1758be3c96167ed0ba8ec929a | the simple formula = i ℏ i , | the simple formula = i ℏ i , {\displaystyle =i\hbar \,\mathbb {i} ~,} valid for the quantization of the simplest classical system, can be generalized to the case of an arbitrary lagrangian l {\displaystyle {\mathcal {l}}}. we identify canonical coordinates (such as x in the example above, or a field Φ(x) in the case of... | wikipedia |
82cf31bb6af516400bb81f8d972d71aa5794b0f1 | a discrete version of the weyl relations, in | a discrete version of the weyl relations, in which the parameters s and t range over z / n {\displaystyle \mathbb {z} /n}, can be realized on a finite-dimensional hilbert space by means of the clock and shift matrices. | wikipedia |
5084717112c61342877691dee59672c0e4ad0309 | for technical reasons, the weyl relations are not | for technical reasons, the weyl relations are not strictly equivalent to the canonical commutation relation = i ℏ {\displaystyle =i\hbar }. if x ^ {\displaystyle {\hat {x}}} and p ^ {\displaystyle {\hat {p}}} were bounded operators, then a special case of the baker–campbell–hausdorff formula would allow one to "exponen... | wikipedia |
f6df32972630d72f3fe0dbf20830adcc82acd8a2 | still, these canonical commutation relations can be rendered | still, these canonical commutation relations can be rendered somewhat "tamer" by writing them in terms of the (bounded) unitary operators exp (i t x ^) {\displaystyle \exp(it{\hat {x}})} and exp (i s p ^) {\displaystyle \exp(is{\hat {p}})}. the resulting braiding relations for these operators are the so-called weyl rel... | wikipedia |
910a9726248f9c62438791c031028c4a4ea9f5cb | alternately, if x ^ {\displaystyle {\hat {x}}} and | alternately, if x ^ {\displaystyle {\hat {x}}} and p ^ {\displaystyle {\hat {p}}} were bounded operators, note that = i ℏ n x ^ n − 1 {\displaystyle =i\hbar n{\hat {x}}^{n-1}}, hence the operator norms would satisfy 2 ‖ p ^ ‖ ‖ x ^ n − 1 ‖ ‖ x ^ ‖ ≥ n ℏ ‖ x ^ n − 1 ‖, {\displaystyle 2\left\|{\hat {p}}\right\|\left\|{\h... | wikipedia |
991ac60df89167466bb0e926e637448612048d6e | according to the standard mathematical formulation of quantum | according to the standard mathematical formulation of quantum mechanics, quantum observables such as x ^ {\displaystyle {\hat {x}}} and p ^ {\displaystyle {\hat {p}}} should be represented as self-adjoint operators on some hilbert space. it is relatively easy to see that two operators satisfying the above canonical com... | wikipedia |
47863eba20239b649a18f18b1bf94bf147c9acf6 | the group h 3 (r) {\displaystyle h_{3}(\mathbb {r})} | the group h 3 (r) {\displaystyle h_{3}(\mathbb {r})} generated by exponentiation of the 3-dimensional lie algebra determined by the commutation relation = i ℏ {\displaystyle =i\hbar } is called the heisenberg group. this group can be realized as the group of 3 × 3 {\displaystyle 3\times 3} upper triangular matrices wit... | wikipedia |
f5a9554ecb49fb88a59dc150ac8a455807315986 | in order for that to reconcile in the | in order for that to reconcile in the classical limit with hamilton's equations of motion, {\displaystyle } must depend entirely on the appearance of p ^ {\displaystyle {\hat {p}}} in the hamiltonian and {\displaystyle } must depend entirely on the appearance of q ^ {\displaystyle {\hat {q}}} in the hamiltonian. furthe... | wikipedia |
94296fd3b6d1eb7a12132c9d140f86af4424c361 | the time derivative of a quantum state is | the time derivative of a quantum state is - i h ^ / ℏ {\displaystyle i{\hat {h}}/\hbar } (by schrödinger equation). equivalently, since the operators are not explicitly time-dependent, they can be seen to be evolving in time (see heisenberg picture) according to their commutation relation with the hamiltonian: d q ^ d ... | wikipedia |
9c48e12d5d824b5eb270d9ddf1f849965af679b7 | in quantum mechanics the hamiltonian h ^ {\displaystyle | in quantum mechanics the hamiltonian h ^ {\displaystyle {\hat {h}}}, (generalized) coordinate q ^ {\displaystyle {\hat {q}}} and (generalized) momentum p ^ {\displaystyle {\hat {p}}} are all linear operators. | wikipedia |
f753dcf96134f2b9b9a91770a3546d360ba87142 | according to the correspondence principle, in certain limits | according to the correspondence principle, in certain limits the quantum equations of states must approach hamilton's equations of motion. the latter state the following relation between the generalized coordinate q (e.g. position) and the generalized momentum p: { q ˙ = ∂ h ∂ p = { q, h }; p ˙ = − ∂ h ∂ q = { p, h }. ... | wikipedia |
eccc39dd37d09a0244a95cd57475071757188fe8 | however, he further appreciated that such a systematic | however, he further appreciated that such a systematic correspondence does, in fact, exist between the quantum commutator and a deformation of the poisson bracket, today called the moyal bracket, and, in general, quantum operators and classical observables and distributions in phase space. he thus finally elucidated th... | wikipedia |
8710351501d81384bf64e6b7cbe311bd1be4936b | this observation led dirac to propose that the | this observation led dirac to propose that the quantum counterparts f ^ {\displaystyle {\hat {f}}}, g ̂ of classical observables f, g satisfy = i ℏ { f, g } ^. {\displaystyle =i\hbar {\widehat {\{f,g\}}}\,.} | wikipedia |
ed2a8098e321425b880a3c0f804458521bcf5c38 | by contrast, in classical physics, all observables commute | by contrast, in classical physics, all observables commute and the commutator would be zero. however, an analogous relation exists, which is obtained by replacing the commutator with the poisson bracket multiplied by i ℏ, { x, p } = 1. {\displaystyle \{x,p\}=1\,.} | wikipedia |
4958d04b6240b3f0b8312ea4baf28b55460079ca | this relation is attributed to werner heisenberg, max | this relation is attributed to werner heisenberg, max born and pascual jordan (1925), who called it a "quantum condition" serving as a postulate of the theory; it was noted by e. kennard (1927) to imply the heisenberg uncertainty principle. the stone–von neumann theorem gives a uniqueness result for operators satisfyin... | wikipedia |
547fff5d038bb7524c042485ebb2a585c2962273 | between the position operator x and momentum operator | between the position operator x and momentum operator p in the x direction of a point particle in one dimension, where = x p − p x is the commutator of x and p , i is the imaginary unit, and ℏ is the reduced planck constant h /2 π, and i {\displaystyle \mathbb {i} } is the unit operator. in general, position and moment... | wikipedia |
b11114845215f54fe712194894182af6d5b0ff29 | in quantum mechanics, the canonical commutation relation is | in quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the fourier transform of another). for example, = i ℏ i {\displaystyle =i\hbar \mathbb {i} } | wikipedia |
261b41c59d6e76486ee380ad2477f893e0c76a5c | joule heating is the process by which the | joule heating is the process by which the passage of an electric current through a conductor produces heat. joule's first law, also known in countries of the former ussr as the joule–lenz law, states that the power of heating generated by an electrical conductor equals the product of its resistance and the square of th... | wikipedia |
859122b67b93568d3d7c7818612d485f34f1355d | some food processing equipment may make use of | some food processing equipment may make use of joule heating: running current through food material causes heat release inside the food. the alternating electrical current coupled with the resistance of the food causes the generation of heat. a higher resistance increases the heat generated. ohmic heating allows for fa... | wikipedia |
58d2206df09f8f53e85fa3d2f1b868c9ac58f965 | the definition of the efficiency of a heating | the definition of the efficiency of a heating process requires defining the boundaries of the system to be considered. when heating a building, the overall efficiency is different when considering heating effect per unit of electric energy delivered on the customer's side of the meter, compared to the overall efficienc... | wikipedia |
cd35c81083662d245490a654e685a25074556f1c | as a heating technology, joule heating has a | as a heating technology, joule heating has a coefficient of performance of 1.0, meaning that every joule of electrical energy supplied produces one joule of heat. in contrast, a heat pump can have a coefficient of more than 1.0 since it moves additional thermal energy from the environment to the heated item. | wikipedia |
af1260b08cb728414d04c56b7b3472e7869c615a | flash joule heating (transient high-temperature electrothermal heating) has | flash joule heating (transient high-temperature electrothermal heating) has been used to synthesize allotropes of carbon, including graphene and diamond. heating various solid carbon feedstocks (carbon black, coal, coffee grounds, etc.) to temperatures of ~3000 k for 10-150 milliseconds produces turbostratic graphene f... | wikipedia |
6b050c08ecc0384693ce9b385914057dc50d6eaa | the potential applications of ohmic heating range from | the potential applications of ohmic heating range from cooking, thawing, blanching, peeling, evaporation, extraction, dehydration, and fermentation. these allow for ohmic heating to pasteurize particulate foods for hot filling, pre-heat products prior to canning, and aseptically process ready-to-eat meals and refrigera... | wikipedia |
a7536f20d24ae02e29412d6bd41f77b6f363256b | ohmic heating is limited by viscosity, electrical conductivity, | ohmic heating is limited by viscosity, electrical conductivity, and fouling deposits. the density of particles within the suspension liquid can limit the degree of processing. a higher viscosity fluid will provide more resistance to heating, allowing the mixture to heat up quicker than low viscosity products. a food pr... | wikipedia |
745c05dc143c4b42eeb574225d0d8d0e88fdc5e1 | decreased processing times in ohmic heating maintains nutritional | decreased processing times in ohmic heating maintains nutritional and sensory properties of foods. ohmic heating inactivates antinutritional factors like lipoxigenase (lox), polyphenoloxidase (ppo), and pectinase due to the removal of active metallic groups in enzymes by the electrical field. similar to other heating m... | wikipedia |
3dcf9696e26e2e6b3e7f81651b8824a35b2c7b86 | microbial inactivation in ohmic heating is achieved by | microbial inactivation in ohmic heating is achieved by both thermal and non-thermal cellular damage from the electrical field. this method destroys microorganisms due to electroporation of cell membranes, physical membrane rupture, and cell lysis. in electroporation, excessive leakage of ions and intramolecular compone... | wikipedia |
2caed9d899a45c907b864af3b760f81d0b222389 | benefits of ohmic heating include: uniform and rapid | benefits of ohmic heating include: uniform and rapid heating (>1°cs), less cooking time, better energy efficiency, lower capital cost, and heating simulataneously throughout food's volume as compared to aseptic processing, canning, and pef. volumetric heating allows internal heating instead of transferring heat from a ... | wikipedia |
205fa421ae58299a3af22e9978eab618a6427f7e | the efficiency by which electricity is converted to | the efficiency by which electricity is converted to heat depends upon on salt, water, and fat content due to their thermal conductivity and resistance factors. in particulate foods, the particles heat up faster than the liquid matrix due to higher resistance to electricity and matching conductivity can contribute to un... | wikipedia |
59257ccffd196a2db7341a23e3fd558041ec0cbc | the generator creates the electrical current which flows | the generator creates the electrical current which flows to the first electrode and passes through the food product placed in the electrode gap. the food product resists the flow of current causing internal heating. the current continues to flow to the second electrode and back to the power source to close the circuit.... | wikipedia |
81a88e73c86028cfa21392af7efd479e0d20db69 | there are different configurations for continuous ohmic heating | there are different configurations for continuous ohmic heating systems, but in the most basic process, a power supply or generator is needed to produce electrical current. electrodes, in direct contact with food, pass electric current through the matrix. the distance between the electrodes can be adjusted to achieve t... | wikipedia |
e24bb25e9385aa3321fe74b2b9df50ccae9e5923 | this method can also inactivate antinutritional factors thereby | this method can also inactivate antinutritional factors thereby maintaining nutritional and sensory properties. however, ohmic heating is limited by viscosity, electrical conductivity, and fouling deposits. although ohmic heating has not yet been approved by the food and drug administration (fda) for commercial use, th... | wikipedia |
5b0c6c1130df9cddc93ed6f3657ceec2134f0bd4 | electrical energy is linearly translated to thermal energy | electrical energy is linearly translated to thermal energy as electrical conductivity increases, and this is the key process parameter that affects heating uniformity and heating rate. this heating method is best for foods that contain particulates suspended in a weak salt containing medium due to their high resistance... | wikipedia |
eb3da497bd95c95987aa207424ca1dce774e3d47 | joule heating is a flash pasteurization (also called | joule heating is a flash pasteurization (also called "high-temperature short-time" (htst)) aseptic process that runs an alternating current of 50–60 hz through food. heat is generated through the food's electrical resistance. as the product heats, electrical conductivity increases linearly. a higher electrical current ... | wikipedia |
c6546cf22cf3f39af577ca095e1d30b495b46384 | usually, a transformer is placed between the lines | usually, a transformer is placed between the lines and consumption. when a high-voltage, low-intensity current in the primary circuit (before the transformer) is converted into a low-voltage, high-intensity current in the secondary circuit (after the transformer), the equivalent resistance of the secondary circuit beco... | wikipedia |
0d818459d6189423e4360c2601a72922a5984763 | the split of power between transmission losses (joule | the split of power between transmission losses (joule heating in transmission lines) and load (useful energy delivered to the consumer) can be approximated by a voltage divider. in order to minimize transmission losses, the resistance of the lines has to be as small as possible compared to the load (resistance of consu... | wikipedia |
c7e769af6ec1b1bfd6920879b88a0f3fcea51091 | in the harmonic case, where all field quantities | in the harmonic case, where all field quantities vary with the angular frequency ω {\displaystyle \omega } as e − i ω t {\displaystyle e^{-\mathrm {i} \omega t}}, complex valued phasors j ^ {\displaystyle {\hat {\mathbf {j} }}} and e ^ {\displaystyle {\hat {\mathbf {e} }}} are usually introduced for the current density... | wikipedia |
4b84eb48ce24c271db6b96670d56f84541e0a45d | here, j {\displaystyle \mathbf {j} } is the | here, j {\displaystyle \mathbf {j} } is the current density, and e {\displaystyle \mathbf {e} } is the electric field. for a material with a conductivity σ {\displaystyle \sigma }, j = σ e {\displaystyle \mathbf {j} =\sigma \mathbf {e} } and therefore d p d v = j ⋅ e = j ⋅ j 1 σ = j 2 ρ {\displaystyle {\frac {\mathrm {... | wikipedia |
5aa934227df8ba07eadf9a9cfa5dcfd5d6c8f885 | where ϕ {\displaystyle \phi } is phase difference | where ϕ {\displaystyle \phi } is phase difference between current and voltage, re {\displaystyle \operatorname {re} } means real part, z is the complex impedance, and y* is the complex conjugate of the admittance (equal to 1/ z*). | wikipedia |
e96da1d9c4ab045de06e5a79ec2a4ab0140f98d6 | p a v g = u rms i | p a v g = u rms i rms cos ϕ = (i rms) 2 re (z) = (u rms) 2 re (y ∗) {\displaystyle p_{\rm {avg}}=u_{\text{rms}}i_{\text{rms}}\cos \phi =(i_{\text{rms}})^{2}\operatorname {re} (z)=(u_{\text{rms}})^{2}\operatorname {re} (y^{*})} | wikipedia |
9e3f6668344483dd64df09f553a33f2c3c737e4b | p a v g = u rms i | p a v g = u rms i rms = (i rms) 2 r = (u rms) 2 / r {\displaystyle p_{\rm {avg}}=u_{\text{rms}}i_{\text{rms}}=(i_{\text{rms}})^{2}r=(u_{\text{rms}})^{2}/r} | wikipedia |
ca86a3a83929b20fb5c11935f0260a853aecc1e4 | assuming the element behaves as a perfect resistor | assuming the element behaves as a perfect resistor and that the power is completely converted into heat, the formula can be re-written by substituting ohm's law, v = i r {\displaystyle v=ir}, into the generalized power equation: p = i v = i 2 r = v 2 / r {\displaystyle p=iv=i^{2}r=v^{2}/r} where r is the resistance. | wikipedia |
d11fa8858586506db068eb0f6fb8ffda66991f9c | joule heating is referred to as ohmic heating | joule heating is referred to as ohmic heating or resistive heating because of its relationship to ohm's law. it forms the basis for the large number of practical applications involving electric heating. however, in applications where heating is an unwanted by-product of current use (e.g., load losses in electrical tran... | wikipedia |
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