Although the resulting energy eigenfunctions ( the orbitals ) are not necessarily isotropic themselves, their dependence on the angular coordinates follows completely generally from this isotropy of the underlying potential: the eigenstates of the Hamiltonian ( that is, the energy eigenstates ) can be chosen as simultaneous eigenstates of the angular momentum operator.

Although chosen in 683, he was not ordained until 684 because the permission of Emperor Constantine IV was not obtained until some months after the election.

Although several billion years old, the Champion is not as intelligent as most other known Elders of the Universe, partially because most have chosen to develop their minds along with their physical bodies.

Although Briggs and Robinson state that eight players will leave with nothing, normally the losing celebrities receive a " house " amount to give to their chosen charity, as well as their own fee for appearing on the show.

Although the new party was dominated by former Nationalists, Lyons was chosen as the new party's leader, and thus became Leader of the Opposition.

Although it showed pride for her many achievements, its use of dialect (" I nebber run my train off de track "), apparently chosen for its authenticity, has been criticized for undermining her stature as an American patriot and dedicated humanitarian.

Although Ahmed Hassan al-Bakr orchestrated the coup, Abdel Salam Arif, a Nasserist, was chosen to be the new president.

Although the UAP was dominated by former Nationalists, Lyons was chosen as leader rather than the Nationalists ' last leader, John Latham.

Although eminently qualified, Komarov was not chosen in the top six candidates, because he did not meet the age, height and weight restrictions specified by the " Chief Designer " of Russia's space program: Sergei Korolev.

Although Richard had been offered Caterina Visconti, one of the daughters of Bernabò Visconti of Milan, who would have brought a great deal of money with her as dowry – Anne was chosen, bringing no direct financial benefits to England.

Although the pairings in a group of 23 people are not statistically equivalent to 253 pairs chosen independently, the birthday paradox becomes less surprising if a group is thought of in terms of the number of possible pairs, rather than as the number of individuals.

Although she appears to have come from a noble family, there is no clear reason as to why she would have been chosen as Leo's bride, leading some scholars to speculate that she was selected in a bride-show, in which eligible women were paraded before the bridegroom, until one was finally selected.

Although some states still maintain electrocution as a method of execution, today it is only maintained as a secondary method that may be chosen over lethal injection at the request of the prisoner.

Although Hull was the oldest and most central of the merged cities, the name Gatineau was chosen for the new city.

Although Hull was the oldest and most central of the merged cities, the name Gatineau was chosen for the new city.

Although different locations were considered for the railroad terminus and shipping port, Agate Bay was chosen because it was closer to the iron ore site and provided a clay bottom bay, while most others were rocky.

Although unsuccessful in his 1958 campaign for California Attorney General, Weinberger continued to be active in politics and was chosen by Nixon in 1962 to become chairman of the California Republican Party.

Although Time Warner eventually let the band go in 1997, they have not signed to another label, and have chosen not to use an independent label, despite showcasing numerous new songs in their live sets.

Although this system was not chosen as a primary candidate for the now-canceled Terrestrial Planet Finder, it was a target star for NASA's proposed Space Interferometry Mission to search for Earth-sized planets.

Although Barry lived his adult life as a man, it is widely believed that he was female assigned at birth and named Margaret Ann Bulkley and that he chose to live as a man so that he might be accepted as a university student and be able to pursue his chosen career as a surgeon.

Although the inductor gives the best performance, usually the resistor is chosen for cost reasons.

Although the Sipahis of the Porte were originally recruited, like the Janissaries, using the devshirmeh system, by the time of Sultan Mehmed II, their ranks were only chosen from among the ethnic Turks who owned land within imperial borders.

Although some of the sampling of items for price collection is done using a sampling frame and probabilistic sampling methods, many items and outlets are chosen in a commonsense way ( purposive sampling ) that does not permit estimation of confidence intervals.

Although the family were very anti-French Gino was chosen with other notables to pay homage to Napoleon in Paris in 1813.

Although the name actually applies to a group of snakes, it is often used to refer only to one species in particular, the common or green anaconda, Eunectes murinus, which is one of the largest snakes in the world.

Although the Indian and Greek concepts of the atom were based purely on philosophy, modern science has retained the name coined by Democritus.

Although Dio is the earliest writer to mention them, Ammianus Marcellinus used the name to refer to Germans on the Limes Germanicus in the time of Trajan's governorship of the province shortly after it was formed, circa 98 / 99.

Although the 1987 decision settled the question of the scientific name of the genus, the common name " amaryllis " continues to be used differently.

Although it is commonly believed that assassins were under the influence of hashish during their killings or during their indoctrination, there is debate as to whether these claims have merit, with many Eastern writers and an increasing number of western academics coming to believe that drug-taking was not the key feature behind the name.

Although this document was subsequently adopted by International Organization for Standardization ( ISO ) and subsequent revisions published by ISO have been adopted by ANSI, the name ANSI C ( rather than ISO C ) is still more widely used.

Although Buzzcut's first name was never given in the series, it was revealed in This Book Sucks.

Although it appears clear that Badminton House, Gloucestershire, owned by the Duke of Beaufort, has given its name to the sports, it is unclear when and why the name was adopted.

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Although the appellation Malachi has frequently been understood as a proper name, its Hebrew meaning is simply " My God's messenger " ( or ' His messenger ' in the Septuagint ) and may not be the author's name at all.

Although his name does not appear in any other part of the Jewish Bible, Rabbinic tradition holds Habakkuk to be the Shunammite woman's son, who was restored to life by Elisha in 2 Kings 4: 16.

Although he must have been familiar with the ancient name, Balcia, meaning a supposed island in the Baltic Sea, and although he may have been aware of the Baltic words containing the stem balt -, " white ", as " swamp ", he reports that he followed the local use of balticus from baelt (" belt ") because the sea stretches to the east " in modum baltei " (" in the manner of a belt ").

Although there is no proof, the name " Thomas Corbett " does appear on the list of dead and missing.

Although the name Chordata is often attributed to William Bateson ( 1885 ), it was already in common use in by 1880.

Although the Garda Síochána had suspicions that the organisation existed, they were unsure of its name, labelling it the " Irish National Republican Army ".

Although positively charged cations always move towards the cathode ( hence their name ) and negatively charged anions move away from it, cathode polarity depends on the device type, and can even vary according to the operating mode.

Although the content of the document file is arranged in a format that the word-processing program understands, the user is able to choose the name and location of the file and provide the bulk of the information ( such as words and text ) that will be stored in the file.

Although his name and history were taken from his early life with his adoptive Earth parents, everything about Clark was staged for the benefit of his alternate identity: as a reporter for the Daily Planet, he receives late-breaking news before the general public, has a plausible reason to be present at crime scenes, and need not strictly account for his whereabouts as long as he makes his story deadlines.

Although Sherlock Holmes is not the original fiction detective ( he was influenced by Poe's Dupin and Gaboriau's Lecoq ), his name has become a byword for the part.

Although he wanted to plead guilty, Justice Samuel Chase urged him to name those who had helped him or subscribed to his writings in exchange for freedom.

Although did not think of himself as a deist, he shared so many attitudes with deists that Gay calls him " a Deist in fact, if not in name ".

Although the Druze consider ad-Darazī a heretic the name had been used to identify them.