mineral deposit: Iron deposits: …Australia, studied deposits in the Hamersley Basin and found that individual thin layers could be traced for more than 100 kilometres. Such continuity suggests that evaporation played a major role in precipitating both the iron minerals and the silica. A second remarkable feature of Lake Superior-type deposits is that they…

Hamersley Range, mountains in the Pilbara region, northwestern Western Australia, extending east-southeast for 160 miles (260 km) south of the Fortescue River. Part of an ancient tableland broken by faults and gorges, the range terminates in rocky headlands and coral islets at the Indian Ocean. It

eastern Africa: The Omani ascendancy: …been to accept the so-called Hamerton Treaty of 1845, by which the export of slaves to his Arabian dominions was forbidden.

horse collar: A hames collar is heavily padded; iron projections (hames) that surround the padding contain eyepieces for the reins and traces.

Judaism: Pilgrim Festivals: …and foods containing leaven (ḥametz) are neither to be owned nor consumed during Pesaḥ. Aside from meats, fresh fruits, and vegetables, it is customary to consume only food prepared under rabbinic supervision and labelled “kosher for Passover,” warranting that they are completely free of contact with leaven. In many…

Hamgyŏng Mountains, mountain range, northeastern North Korea. The range forms a watershed that separates the northern frontier area along the Chinese border from the eastern Sea of Japan (East Sea) area. The Hamgyŏng Mountains lie on the northeastern edge of the Kaema Highlands and stretch

Hamgyŏng Mountains, mountain range, northeastern North Korea. The range forms a watershed that separates the northern frontier area along the Chinese border from the eastern Sea of Japan (East Sea) area. The Hamgyŏng Mountains lie on the northeastern edge of the Kaema Highlands and stretch

Hamhŭng, city, capital of South Hamgyŏng do (province), east-central North Korea. It was the commercial and local administrative centre of northeastern Korea during the Chosŏn dynasty (1392–1910). It began to develop rapidly as a modern industrial city with the construction in 1928 of a large

Hami, city and oasis, eastern Uygur Autonomous Region of Xinjiang, China. An important stage on the roads from Gansu province into Central Asia and to the west, Hami was known to the Chinese in early times as Yiwu, the name Hami being the Chinese rendering of the Mongolian version (Khamil) of the

Tien Shan: Physiography: …the Turfan Depression is the Hami (Qomul) Basin; both basins are bounded to the north by the Bogda Mountains, with elevations of up to 17,864 feet (5,445 metres), and by the eastern extremity of the Tien Shan, the Karlik Mountains, which reach a maximum elevation of 16,158 feet (4,925 metres).

Hamid Dynasty, Turkmen dynasty (c. 1300–1423) that ruled in southwestern Anatolia. It was founded by Felekuddin Dündar, whose father, Ilyas, was a frontier ruler under the Seljuqs and who named it after his grandfather; Dündar governed the Hamid principality jointly with his brother Yunus, with two

withdrawal of United States troops from Afghanistan: U.S.-Taliban peace agreement and withdrawal: …nationals to rush to the international airport in Kabul. Many had fought the Taliban or had supported Afghan or NATO forces. In the last few weeks before the August 31 deadline, the United States focused its attention on evacuating refugees. With the joint goal of seeing U.S. withdrawal to its…

Isparta, city, western Turkey. It is located at the western end of the Taurus Mountains. Known as Baris under the Byzantine Empire, it was taken by the Seljuq Turks in 1203–04. Later it belonged to the Turkmen Hamid principality, the last ruler of which sold it to the Ottoman sultan about 1381. The

12 Extraordinary Women in the Mughal Empire: Hamida Banu Begum (wife of Humayun and mother of Akbar): The teenage Hamida Banu Begum married Humayun in 1541, after he had been dispossessed by Sher Shah, and endured the vagaries of exile with him for nearly 15 years. She gave birth to Akbar while the depleted Mughal entourage meandered toward Afghanistan.

Isparta, city, western Turkey. It is located at the western end of the Taurus Mountains. Known as Baris under the Byzantine Empire, it was taken by the Seljuq Turks in 1203–04. Later it belonged to the Turkmen Hamid principality, the last ruler of which sold it to the Ottoman sultan about 1381. The

Hamidian massacres, series of atrocities carried out by Ottoman forces and Kurdish irregulars against the Armenians in the Ottoman Empire between 1894 and 1896. They are generally called the Hamidian massacres—after the Ottoman Sultan Abdülhamid II, during whose reign they were carried out—to

Hamilcar Barca was a general who assumed command of the Carthaginian forces in Sicily during the last years of the First Punic War with Rome (264–241 bce). Until the rise to power of his son Hannibal, Hamilcar was the finest commander and statesman that Carthage had produced. Nothing is known of

Dorothy Hamill: Early life and Olympics: Hamill invented the Hamill camel, a camel spin that is followed by a sit spin.

Dorothy Hamill is an American former figure skater who won the gold medal for women’s figure skating in the 1976 Olympic Winter Games in Innsbruck, Austria. Hamill later worked as a TV commentator. (Read Scott Hamilton’s Britannica entry on figure skating.) Hamill first skated at age eight on a

Dorothy Hamill is an American former figure skater who won the gold medal for women’s figure skating in the 1976 Olympic Winter Games in Innsbruck, Austria. Hamill later worked as a TV commentator. (Read Scott Hamilton’s Britannica entry on figure skating.) Hamill first skated at age eight on a

American actor Mark Hamill has the distinction of having resisted typecasting so successfully that the two defining roles of his career—the heroic Luke Skywalker of the Star Wars franchise and the animated version of the DC Comics supervillain the Joker—occupy extreme ends of the moral spectrum.

Hamilton, city in the fertile western region of Victoria, Australia, on the Grange Burn River. The original village (founded in 1850) grew around an inn on the north bank of the river and was called The Grange. It became an important way station for coach traffic in the 1850s between Portland and

Hamilton, large burgh (town), South Lanarkshire council area, historic county of Lanarkshire, west-central Scotland, situated near the junction of Avon Water and the River Clyde, just southeast of the metropolitan complex of Glasgow. The area has been settled since prehistoric times. Cadzow Castle,

Lin-Manuel Miranda: A filmed performance of Hamilton aired on television in 2020.

Hamilton, county, northeastern New York state, U.S., consisting of a mountainous region located in the centre of Adirondack Park (1892), which is one of the largest parks in the United States and the nation’s first forest preserve. The area is heavily wooded with spruce and balsam fir trees.

Hamilton, city, seat (1803) of Butler county, southwestern Ohio, U.S., on the Great Miami River, about 25 miles (40 km) north of Cincinnati. In 1794 a town called Fairfield was laid out adjoining Fort Hamilton, which was used in 1791–96 by Gen. Arthur St. Clair and Gen. “Mad” Anthony Wayne against

Hamilton, city, southeastern Ontario, Canada. It lies at the extreme western end of Lake Ontario, on the southern shore of landlocked Hamilton Harbour (Burlington Bay). The site was visited by the French explorer René-Robert Cavelier, sieur de La Salle, in 1669. Settlement began with the arrival of

Hamilton, stage musical by American composer and lyricist Lin-Manuel Miranda that premiered Off-Broadway on February 17, 2015, at the Public Theater in New York City before moving to Broadway for a second opening on August 6. Based on the life of Alexander Hamilton, the explosively popular,

Hamilton, capital of the British overseas territory of Bermuda. It lies on Main Island (Great Bermuda) in the western Atlantic Ocean, along the northern shore of a deepwater harbour. The name also applies to one of the nine parishes on the island. Founded in 1790 and incorporated in 1793, Hamilton

Hamilton, city, Waikato regional council, north-central North Island, New Zealand. It lies 80 miles (130 km) above the mouth of the Waikato River. Hamilton originated as a military settlement on the site of a deserted Maori village. Declared a borough in 1877 and a city in 1945, it was named for

graph theory: …path, later known as a Hamiltonian circuit, along the edges of a dodecahedron (a Platonic solid consisting of 12 pentagonal faces) that begins and ends at the same corner while passing through each corner exactly once. The knight’s tour (see number game: Chessboard problems) is another example of a recreational…

Hamilton College, private, coeducational institution of higher learning in Clinton, New York, U.S. It is a liberal arts college and offers a curriculum in the humanities, social sciences, life sciences, and physical sciences. It awards the bachelor’s degree. Students can choose to study abroad in a

Allan Nevins: …Study in Courage (1932) and Hamilton Fish, The Inner History of the Grant Administration (1936). In 1948 he inaugurated the oral history movement in the United States, establishing at Columbia a project for preserving on tape interviews with notable figures whose views of current affairs would interest future historians.

Hamilton: …its constituent galleries, and the Hamilton Gardens, a multifunctional facility featuring botanical displays, public art, educational programs, and special events facility. Pop. (2006) 155,262; (2012 est.) 176,900.

Colgate University, private, coeducational institution of higher learning in Hamilton, New York, U.S. The university offers a liberal arts curriculum for undergraduates and several master’s degree programs. Campus facilities include an automated observatory, the Dana Arts Center, and the Longyear

William Hamilton of Gilbertfield was a Scottish writer whose vernacular poetry is among the earliest in the 18th-century Scottish literary revival. After serving in the British Army, he retired to the life of a country gentleman. He became closely acquainted with the poet Allan Ramsay, with whom he

Churchill River, largest river of Labrador, Newfoundland, Canada. It is formed from several river-lakes on the central plateau of western Labrador (a region of extensive iron-ore development) and meanders more than 200 miles (300 km) to Churchill Falls. There, the course is broken by a series of

United Technologies Corporation: Hamilton Sundstrand: Luttrell) to form Hamilton Standard Propeller Corporation. Hamilton Standard became the leading maker of aircraft propellers, producing more than 500,000 during World War II.

Margaret Hamilton: …Software in 1976 and established Hamilton Technologies 10 years later.

Canadian Football League: …the East Division are the Hamilton Tiger-Cats, Ottawa Redblacks, Montreal Alouettes, and Toronto Argonauts.

Canadian Football League: …the East Division are the Hamilton Tiger-Cats, Ottawa Redblacks, Montreal Alouettes, and Toronto Argonauts.

mechanics: Lagrange’s and Hamilton’s equations: …even more powerful method called Hamilton’s equations. It begins by defining a generalized momentum p i , which is related to the Lagrangian and the generalized velocity q̇ i by p i = ∂L/∂q̇ i . A new function, the Hamiltonian, is then defined by H = Σi q̇ i…

principles of physical science: Manifestations of the extremal principle: …the Irish mathematician and scientist William Rowan Hamilton in 1835. Though very general, it is well enough illustrated by a simple example, the path taken by a particle between two points A and B in a region where the potential ϕ(r) is everywhere defined. Once the total energy E of…

Hamilton’s rule, in ecology and sociobiology, mathematical formula devised by British naturalist and population geneticist W.D. Hamilton that supports the notion that natural selection favours genetic success, not reproductive success per se. It recognizes that individuals can pass copies of their

Alexander Hamilton was a New York delegate to the Constitutional Convention (1787), major author of the Federalist papers, and first secretary of the treasury of the United States (1789–95), who was the foremost champion of a strong central government for the new United States. He was killed in a

Alice Hamilton was an American pathologist, known for her research on industrial diseases. Hamilton received her medical degree from the University of Michigan (1893) and continued her studies at Johns Hopkins University and in Germany. From 1897 to 1919 she was a resident of Hull House in Chicago.

Andrew Hamilton was a British American colonial lawyer, judge, and public official who defended John Peter Zenger in a case important as the first victory for freedom of the press in the American colonies (1735). Hamilton is known to have migrated to Virginia as an indentured servant shortly before

Ann Hamilton is an American installation artist who created performance art, physical objects, video and audio works, photographic prints, public art projects, site-specific sense-intensive installations, and other types of art. Working across multiple platforms to engage the viewer on several

Patrick Hamilton was an English playwright and novelist, notable for his capture of atmosphere and the Cockney dialect traditionally associated with the East End of London. Hamilton began acting in 1921 and then, fascinated by theatrical melodrama, took to writing. He became known with the novel

Bethany Hamilton is an American professional surfer, author, and motivational speaker who lost her arm to a shark while surfing when she was 13 years old. She served as an inspiration to people when she returned to surfing shortly after the attack, despite her serious injury. Bethany Hamilton is

Bethany Hamilton is an American professional surfer, author, and motivational speaker who lost her arm to a shark while surfing when she was 13 years old. She served as an inspiration to people when she returned to surfing shortly after the attack, despite her serious injury. Bethany Hamilton is

Matt Helm: …novels (1960–83) by American writer Donald Hamilton. Employed by a secret military organization during World War II, Helm is called upon to spy, to kill, and to convey military secrets. The character was portrayed by Dean Martin in four films of the late 1960s and by Tony Franciosa in a…

Edith Hamilton was an American educator and author who was a notable popularizer of classical literature. Born in Germany of American parents, Hamilton grew up in Fort Wayne, Indiana. Her sister Alice was two years her junior. From an early age Edith was an eager student of Greek and Roman

Emma, Lady Hamilton was the mistress of the British naval hero Admiral Horatio (afterward Viscount) Nelson. The daughter of a blacksmith, she was calling herself Emily Hart when, in 1781, she began to live with Charles Francis Greville, nephew of her future husband, Sir William Hamilton, British

Mary Abigail Dodge was an American essayist and editor whose writings included works both of homely wit and in ardent support of women’s independence from men. In 1850 Dodge graduated from the Ipswich (Massachusetts) Female Seminary, and she remained there as a teacher until 1854. She taught

Gavin Hamilton was a Scottish-born painter of scenes from history, portraitist, archaeologist, and art dealer who was one of the pioneers of Neoclassicism. From 1742 until his death he lived in Rome, except for a period from about 1752 to 1754 when he was in London, primarily painting portraits of

Hamish Hamilton was a British publisher who published works by some of the most renowned authors in Britain, the United States, and France. Hamilton studied modern languages and law at Caius College, Cambridge, and gained national attention as a champion oarsman in the Grand Challenge Cup (1927 and

Hamish Hamilton was a British publisher who published works by some of the most renowned authors in Britain, the United States, and France. Hamilton studied modern languages and law at Caius College, Cambridge, and gained national attention as a champion oarsman in the Grand Challenge Cup (1927 and

James Hamilton, 3rd marquess and 1st duke of Hamilton was a Scottish Royalist whose vacillating, ineffectual leadership did great damage to King Charles I’s cause during the English Civil Wars between the Royalists and the Parliamentarians. Educated at Oxford University, he succeeded to his

James Hamilton, 3rd marquess and 1st duke of Hamilton was a Scottish Royalist whose vacillating, ineffectual leadership did great damage to King Charles I’s cause during the English Civil Wars between the Royalists and the Parliamentarians. Educated at Oxford University, he succeeded to his

Scotland: Mary (1542–67) and the Scottish Reformation: For example, Archbishop John Hamilton, a would-be reformer who gave his name to a vernacular catechism (1552), belonged to the family who had the most to lose if the careerists were curbed.

John Hamilton, 1st marquess of Hamilton was a Scottish nobleman active in Scottish and English politics and in the unsuccessful negotiations for the release of Mary Stuart, Queen of Scots. The third son of James Hamilton, 2nd earl of Arran, he was given the abbey of Arbroath in 1551. In politics he

John Hamilton, 1st marquess of Hamilton was a Scottish nobleman active in Scottish and English politics and in the unsuccessful negotiations for the release of Mary Stuart, Queen of Scots. The third son of James Hamilton, 2nd earl of Arran, he was given the abbey of Arbroath in 1551. In politics he

Georgia O’Keeffe: Life after Stieglitz: …her friend and associate, sculptor Juan Hamilton, she completed her autobiography, Georgia O’Keeffe (1976), and participated in a film about her life and art, Georgia O’Keeffe (1977). Hamilton also taught her to work with clay, and, with assistance, she produced objects in this medium and in watercolour, while working independently…

9-11 Commission: …Thomas Kean and former congressman Lee Hamilton subsequently agreed to chair and vice-chair the commission, which was composed of five Republicans and five Democrats. A staff of experts led by Philip Zelikow prepared the report after interviewing 1,200 individuals and studying thousands of classified and unclassified reports. Nineteen days of…

Lewis Hamilton is one of the most successful Formula One (F1) Grand Prix racing drivers of all time. He owns the F1 record for career race victories and is tied with Michael Schumacher for the most drivers’ championships (seven). In 2008 he became the first Black driver to win the F1 world drivers’

Lewis Hamilton is one of the most successful Formula One (F1) Grand Prix racing drivers of all time. He owns the F1 record for career race victories and is tied with Michael Schumacher for the most drivers’ championships (seven). In 2008 he became the first Black driver to win the F1 world drivers’

The Terminator: …kill Sarah Connor (played by Linda Hamilton), a woman whose unborn son will lead the future fight against an artificial intelligence system’s attempt to destroy humanity. The film was a huge box office success, grossing more than $78 million worldwide, and is credited with launching Cameron’s career as well as…

The Wizard of Oz: Plot summary: …Witch of the West (Margaret Hamilton), vows to kill Dorothy in order to avenge her sister and retrieve the powerful ruby slippers. Glinda the Good Witch (Billie Burke) instructs Dorothy to follow the yellow brick road that runs to the Emerald City, where it is said that a powerful…

Margaret Hamilton is an American computer scientist who was one of the first computer software programmers; she created the term software engineer to describe her work. She helped write the computer code for the command and lunar modules used on the Apollo missions to the Moon in the late 1960s and

The Graduate: Cast: Assorted References

Patrick Hamilton was an English playwright and novelist, notable for his capture of atmosphere and the Cockney dialect traditionally associated with the East End of London. Hamilton began acting in 1921 and then, fascinated by theatrical melodrama, took to writing. He became known with the novel

Grigori Perelman: In 1982 the American mathematician Richard Hamilton took up the idea of studying how a manifold develops as its curvature is smoothed out, using what is known as a Ricci flow (after the Italian mathematician Gregorio Ricci-Curbastro). Much was achieved, but Hamilton reached an impasse when he could not show…

Western painting: Pop art in Britain and the United States: the 1960s: …of their main artist member, Richard Hamilton. Hence, in a work such as $he (1958–61), he combined allusions to fine art (Duchamp again) with esoteric references to American television advertising aimed at women. Another key member of the Independent Group was Edouardo Paolozzi, who had famously lectured to the group…

Western painting: Pop art in Britain and the United States: the 1960s: …of their main artist member, Richard Hamilton. Hence, in a work such as $he (1958–61), he combined allusions to fine art (Duchamp again) with esoteric references to American television advertising aimed at women. Another key member of the Independent Group was Edouardo Paolozzi, who had famously lectured to the group…

Scott Hamilton is an American figure skater who was a four-time world champion and the 1984 Olympic gold medal winner in men’s figure skating. He has been credited with imbuing men’s figure skating with an air of athleticism. In order to portray figure skating as a sport, he took to the ice in the

Sir Denis Hamilton was a British newspaper editor who led the postwar campaign for broader media coverage and more innovative journalism. After serving on Field Marshal B.L. Montgomery’s staff during World War II, Hamilton worked as the personal assistant to the British newspaper magnate Lord

Sir Denis Hamilton was a British newspaper editor who led the postwar campaign for broader media coverage and more innovative journalism. After serving on Field Marshal B.L. Montgomery’s staff during World War II, Hamilton worked as the personal assistant to the British newspaper magnate Lord

Sir Ian Hamilton was a British general, commander in chief of the Mediterranean Expeditionary Force in the unsuccessful campaign against Turkey in the Gallipoli Peninsula during World War I. Hamilton joined the army in 1872, transferring to the 92nd Highlanders and serving with them in the Second

Sir Ian Hamilton was a British general, commander in chief of the Mediterranean Expeditionary Force in the unsuccessful campaign against Turkey in the Gallipoli Peninsula during World War I. Hamilton joined the army in 1872, transferring to the 92nd Highlanders and serving with them in the Second

Sir William Hamilton was a British diplomat and archaeologist. He was the husband of Emma, Lady Hamilton, the mistress of Admiral Horatio Nelson. Hamilton was the son of Lord Archibald Hamilton, governor of Jamaica. He served in the army (1747–58) but left it after his marriage to a Welsh heiress,

Sir William Rowan Hamilton was an Irish mathematician who contributed to the development of optics, dynamics, and algebra—in particular, discovering the algebra of quaternions. His work proved significant for the development of quantum mechanics. Hamilton was the son of a solicitor. He was educated

Sir William Hamilton, 9th Baronet was a Scottish metaphysical philosopher and influential educator, also remembered for his contributions in the field of logic. Hamilton took his B.A. from Balliol College, Oxford, in 1811 and became a member of the Scottish bar in 1813. He inherited a baronetcy in

Dunblane school massacre: The attack: The gunman, Thomas Hamilton, lived in the town. On the day of the massacre, he drove into the school parking lot at about 9:30 in the morning. He cut the cables on a telephone pole and then entered the school, carrying four handguns and 743 rounds of…

Aerosmith: …23, 1952, Winchester, Massachusetts), bassist Tom Hamilton (b. December 31, 1951, Colorado Springs, Colorado), and drummer Joey Kramer (b. June 21, 1950, New York City).

William Donald Hamilton was a British naturalist and population geneticist who found solutions to two of Darwin’s outstanding problems: the evolution of altruism and the evolution of sexual reproduction. Hamilton’s work on the genetics of social behaviour inspired the sociobiology debate of the

William Donald Hamilton was a British naturalist and population geneticist who found solutions to two of Darwin’s outstanding problems: the evolution of altruism and the evolution of sexual reproduction. Hamilton’s work on the genetics of social behaviour inspired the sociobiology debate of the

William Hamilton, 2nd duke of Hamilton was a Scottish Royalist during the English Civil Wars, who succeeded to the dukedom on the execution of his brother, the 1st duke, in 1649. He was a loyal follower of his brother and was created earl of Lanark in 1639; in the next year he became secretary of

William Hamilton, 2nd duke of Hamilton was a Scottish Royalist during the English Civil Wars, who succeeded to the dukedom on the execution of his brother, the 1st duke, in 1649. He was a loyal follower of his brother and was created earl of Lanark in 1639; in the next year he became secretary of

William Thomas Hamilton was a mountain man, trapper, and scout of the American West. Brought to America at age two, Hamilton grew up in St. Louis, Mo., and began trapping at an early age on the North Platte and Green rivers (in present-day Nebraska and Wyoming). He became an Indian fighter in the

Burr-Hamilton duel, duel fought between U.S. Vice Pres. Aaron Burr and Alexander Hamilton, former first secretary of the U.S. Treasury, on July 11, 1804, in Weehawken, New Jersey, that resulted in the death of Hamilton the following day. The two men had long been political rivals, but the immediate

George Hamilton-Gordon, 4th earl of Aberdeen was a British foreign secretary and prime minister (1852–55) whose government involved Great Britain in the Crimean War against Russia (1853–56). Orphaned at age 11, George Gordon (who added his deceased first wife’s family name to his own surname in

Pierre-Louis Lions: …he introduced “viscosity solutions” for Hamilton-Jacobi equations, equations that had been the subject of his doctoral dissertation, where he had found solutions using techniques from partial differential equations and probability. Later, with R.J. DiPerna, Lions rigorously demonstrated the existence of solutions to Boltzmann’s equation for the density of colliding hard…

Hamilton College, private, coeducational institution of higher learning in Clinton, New York, U.S. It is a liberal arts college and offers a curriculum in the humanities, social sciences, life sciences, and physical sciences. It awards the bachelor’s degree. Students can choose to study abroad in a

Frederick Temple Hamilton-Temple-Blackwood, 1st marquess of Dufferin and Ava was a British diplomat who was a distinguished governor-general of Canada and viceroy of India. The son of the 4th Baron Dufferin, he was educated at Eton and Christ Church College, Oxford. He held undersecretaryships in

Caroline Blackwood was an Irish journalist and novelist whose psychological fiction examines physical and emotional deformity. She was married at different times to the British artist Lucian Freud and the American poet Robert Lowell. Blackwood, a descendant of the 18th-century dramatist Richard

William Donald Hamilton: …Zuk, Hamilton also developed the Hamilton-Zuk hypothesis of sexual selection, which explains the evolutionary benefit behind the female preference for healthy, parasite-free males.

Hamiltonian function, mathematical definition introduced in 1835 by Sir William Rowan Hamilton to express the rate of change in time of the condition of a dynamic physical system—one regarded as a set of moving particles. The Hamiltonian of a system specifies its total energy—i.e., the sum of its

graph theory: …path, later known as a Hamiltonian circuit, along the edges of a dodecahedron (a Platonic solid consisting of 12 pentagonal faces) that begins and ends at the same corner while passing through each corner exactly once. The knight’s tour (see number game: Chessboard problems) is another example of a recreational…

Hamiltonian function, mathematical definition introduced in 1835 by Sir William Rowan Hamilton to express the rate of change in time of the condition of a dynamic physical system—one regarded as a set of moving particles. The Hamiltonian of a system specifies its total energy—i.e., the sum of its