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Wave Function
In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi (letter), psi, respectively). Wave functions are complex number, complex-valued. For example, a wave function might assign a complex number to each point in a region of space. The Born rule provides the means to turn these complex probability amplitudes into actual probabilities. In one common form, it says that the squared modulus of a wave function that depends upon position is the probability density function, probability density of measurement in quantum mechanics, measuring a particle as being at a given place. The integral of a wavefunction's squared modulus over all the system's degrees of freedom must be equal to 1, a condition called ''normalization''. Since the wave function is complex-valued, only its relative phase and relative magnitud ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BC. It was derived from the earlier Phoenician alphabet, and is the earliest known alphabetic script to systematically write vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BC, the Ionia, Ionic-based Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard throughout the Greek-speaking world and is the version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , , , , , , , The Greek alphabet is the ancestor of several scripts, such as the Latin script, Latin, Gothic alphabet, Gothic, Coptic script, Coptic, and Cyrillic scripts. Throughout antiquity, Greek had only a single uppercas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Western Greek Alphabet
Many local variants of the Greek alphabet were employed in ancient Greece during the Archaic Greece, archaic and Classical Greece, early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms of the Greek alphabet were originally based on the shared inventory of the 22 symbols of the Phoenician alphabet, with the exception of the letter Samekh, whose Greek counterpart Xi (letter), Xi () was used only in a subgroup of Greek alphabets, and with the common addition of Upsilon () for the vowel . The local, so-called ''epichoric'', alphabets differed in many ways: in the use of the consonant symbols , and ; in the use of the innovative long vowel letters ( and ), in the absence or presence of Η in its original consonant function (); in the use or non-use of certain archaic letters ( = , = , = ); and in many details of the individual shapes of each letter. The system now familiar as the standa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Algiz
Algiz (also Elhaz) is the name conventionally given to the "''z''-rune" of the Elder Futhark runic alphabet. Its transliteration is ''z'', understood as a phoneme of the Proto-Germanic language, the terminal ''*z'' continuing Proto-Indo-European language, Proto-Indo-European terminal ''*s'' via Verner's law. It is one of two runes which express a phoneme that does not occur word-initially, and thus could not be named Acrophony, acrophonically, the other being the ''ŋ''-rune Ingwaz rune, Ingwaz . As the terminal ''*-z'' phoneme marks the nominative singular suffix of masculine nouns, the rune occurs comparatively frequently in Elder Futhark inscriptions, early epigraphy. Because this specific phoneme was lost at an early time, the Elder Futhark rune underwent changes in the medieval runic alphabets. In the Anglo-Saxon runes, Anglo-Saxon futhorc it retained its shape, but became otiose as it ceased to represent any sound in an Old English. However, possibly due to runic manuscr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, is a numeral system, system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal number (linguistics), ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal number (linguistics), cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoans, Minoan and Mycenaean civilizations' Linear A and Linear B alphabets used a different system, called Aegean numerals, which included number-only symbols for powers of ten: = 1, = 10, = 100, = 1000, and = 10000. Attic numerals composed another system that came into use perhaps in the 7th century BC. They were acrophonic, derived (after the initial one) from the first letters of the names of the numbers represented. They ran = 1, = ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psi (Cyrillic)
Psi (Ѱ, ѱ; italics: ) is a letter in the early Cyrillic alphabet, derived from the Greek letter of the same name (Ψ, ψ). It represents the sound /ps/, as in English ''naps''. According to the school rules developed in the 16th and the 17th centuries, such as Meletius Smotrytsky's grammar book, it was intended for use in words of Greek origin, but it was occasionally used for writing native words as well like Ukrainian (''psy'', "dogs").Simovyč 1963, p 515a. It was used especially in words relating to the Eastern Orthodox Eastern Orthodoxy, otherwise known as Eastern Orthodox Christianity or Byzantine Christianity, is one of the three main Branches of Christianity, branches of Chalcedonian Christianity, alongside Catholic Church, Catholicism and Protestantism ... Church, as can be seen in its continuing use in Church Slavonic. Psi was eliminated from the Russian orthography, along with ksi, omega, and the yuses, in the Civil Script of 1708 ( Peter the Great' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bra–ket Notation
Bra–ket notation, also called Dirac notation, is a notation for linear algebra and linear operators on complex vector spaces together with their dual space both in the finite-dimensional and infinite-dimensional case. It is specifically designed to ease the types of calculations that frequently come up in quantum mechanics. Its use in quantum mechanics is quite widespread. Bra–ket notation was created by Paul Dirac in his 1939 publication ''A New Notation for Quantum Mechanics''. The notation was introduced as an easier way to write quantum mechanical expressions. The name comes from the English word "bracket". Quantum mechanics In quantum mechanics and quantum computing, bra–ket notation is used ubiquitously to denote quantum states. The notation uses angle brackets, and , and a vertical bar , to construct "bras" and "kets". A ket is of the form , v \rangle. Mathematically it denotes a vector, \boldsymbol v, in an abstract (complex) vector space V, and physicall ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Italic Alphabets
The Old Italic scripts are a family of ancient writing systems used in the Italian Peninsula between about 700 and 100 BC, for various languages spoken in that time and place. The most notable member is the Etruscan alphabet, which was the immediate ancestor of the Latin alphabet used by more than 100 languages today, including English. The runic alphabets used in Northern Europe are believed to have been separately derived from one of these alphabets by the 2nd century AD. Origins The Old Italic alphabets ultimately derive from the Phoenician alphabet, but the general consensus is that the Etruscan alphabet was imported from the Euboean Greek colonies of Cumae and Ischia (Pithekoūsai) situated in the Gulf of Naples in the 8th century BC; this Euboean alphabet is also called 'Cumaean' (after Cumae), or 'Chalcidian' (after its metropolis Chalcis). The Cumaean hypothesis is supported by the 1957–58 excavations of Veii by the British School at Rome, which found pie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Early Cyrillic Alphabet
The Early Cyrillic alphabet, also called classical Cyrillic or paleo-Cyrillic, is an alphabetic writing system that was developed in Medieval Bulgaria in the Preslav Literary School during the late 9th century. It is used to write the Church Slavonic language, and was historically used for its ancestor, Old Church Slavonic. It was also used for other languages, but between the 18th and 20th centuries was mostly replaced by the modern Cyrillic script, which is used for some Slavic languages (such as Russian language, Russian), and for East European and Asian languages that have experienced a great amount of Russian cultural influence. History The earliest form of manuscript Cyrillic, known as ''Ustav (script), ustav'', was based on Uncial script, Greek uncial script, augmented by typographic ligature, ligatures and by letters from the Glagolitic alphabet for phonemes not found in Greek. The Glagolitic script was created by the Byzantine monk Saints Cyril and Methodius, Sa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychology
Psychology is the scientific study of mind and behavior. Its subject matter includes the behavior of humans and nonhumans, both consciousness, conscious and Unconscious mind, unconscious phenomena, and mental processes such as thoughts, feelings, and motivation, motives. Psychology is an academic discipline of immense scope, crossing the boundaries between the Natural science, natural and social sciences. Biological psychologists seek an understanding of the Emergence, emergent properties of brains, linking the discipline to neuroscience. As social scientists, psychologists aim to understand the behavior of individuals and groups.Hockenbury & Hockenbury. Psychology. Worth Publishers, 2010. A professional practitioner or researcher involved in the discipline is called a psychologist. Some psychologists can also be classified as Behavioural sciences, behavioral or Cognitive science, cognitive scientists. Some psychologists attempt to understand the role of mental functions in i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a partial differential equation that governs the wave function of a non-relativistic quantum-mechanical system. Its discovery was a significant landmark in the development of quantum mechanics. It is named after Erwin Schrödinger, an Austrian physicist, who postulated the equation in 1925 and published it in 1926, forming the basis for the work that resulted in his Nobel Prize in Physics in 1933. Conceptually, the Schrödinger equation is the quantum counterpart of Newton's second law in classical mechanics. Given a set of known initial conditions, Newton's second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of the wave function, the quantum-mechanical characterization of an isolated physical system. The equation was postulated by Schrödinger based on a postulate of Louis de Broglie that all matter has an associated matter wave. The equati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Qubit
In quantum computing, a qubit () or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state (or two-level) quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states (left-handed and the right-handed circular polarization) can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing. Etymology The coining of the term ''qubit'' is attributed to Benjamin Schumacher. In the acknow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
