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Wave Function
A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters and (lower-case and capital psi, respectively). The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state. For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance, it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier tran ... [...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 BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for 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 BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin script, Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin ... [...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 and 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 () was used only in a sub-group 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 standard 24-letter Greek alphabet was originally ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bra–ket Notation
In quantum mechanics, bra–ket notation, or Dirac 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 physically it represents a state of some quantum system. A bra is of the form \langle f, . Mathematically it denotes a linear form f:V \to \Complex, i.e. a linear map that maps each vector in V to a number in the complex plane \Complex. Letting the linear functional \langle f, act on a vector , v\rangle is written as \langle f , v\rangle \in \Complex. Assume that on V there exists an inner product (\cdot,\cdot) with antilinear first argument, which makes V an inner product space. Then with this inner product each vector \boldsymbol \phi \equiv , \phi\rangle can be identified with a corresponding linear form, by placing the vector in the anti-line ... [...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 psi (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 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's ''Grazhdansky Shrift''), and it has also been dropped from other secular languages. It continues to be used in Church Slavonic. Computing codes See also * Psi (other) Psi, PSI or Ψ may refer to: Alphabetic letters * Psi (Greek) (Ψ, ψ), the 23rd l ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Old Italic Alphabets
The Old Italic scripts are a family of similar ancient writing systems used in the Italy, 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 currently used by English language, English and many other languages of the world. 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 clearly derive from the Phoenician alphabet, although the precise chain of cultural transmission is unknown. Some scholars argue that the Etruscan alphabet was imported from the Euboean Greek colonisation, Greek colonies of Cumae and Ischia, Ischia (Pithekoūsai) in the Gulf of Naples in the 8th century BC; this Archaic Greek alphabets#Euboean, Euboean alphabet is also called 'Cumaean' (after Cumae), or 'Chalcidia ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoan and Mycenaean civilization Mycenaean Greece (or the Mycenaean civilization) was the last phase of the Bronze Age in Ancient Greece, spanning the period from approximately 1750 to 1050 BC.. It represents the first advanced and distinctively Greek civilization in mainland ...s' 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 comprised another system that came into use perhaps in th ... [...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 terminal ''*s''. It is one of two runes which express a phoneme that does not occur word-initially, and thus could not be named acrophonically, the other being the ''ŋ''-rune Ingwaz . As the terminal ''*-z'' phoneme marks the nominative singular suffix of masculine nouns, the rune occurs comparatively frequently in 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 futhorc it retained its shape, but it was given the sound value of Latin ''x''. This is a secondary development, possibly due to runic manuscript tradition, and there is no known instance of the rune being used in an Old English inscription. In Proto-Nors ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Early Cyrillic Alphabet
The Early Cyrillic alphabet, also called classical Cyrillic or paleo-Cyrillic, is a writing system that was developed in the First Bulgarian Empire during the late 9th century on the basis of the Greek alphabet for the Slavic people living near the Byzantine Empire in South East and Central Europe. It was used by Slavic peoples in South East, Central and Eastern Europe. It was developed in the Preslav Literary School in the capital city of the First Bulgarian Empire in order to write the Old Church Slavonic language. The modern Cyrillic script is still used primarily for some Slavic languages (such as Bulgarian, Macedonian, Serbian, Russian and Ukrainian), Kazakhstanand for East European and Asian languages that have experienced a great amount of Russian cultural influence. Among some of the traditionally culturally influential countries using Cyrillic script are Bulgaria, Russia, Serbia and Ukraine. Set А Б В Г Д Є Ж З И І К Л М Н О П Р С Т Ꙋ Ф Х ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Psychology
Psychology is the scientific study of mind and behavior. Psychology includes the study of conscious and unconscious phenomena, including feelings and thoughts. It is an academic discipline of immense scope, crossing the boundaries between the natural and social sciences. Psychologists seek an understanding of the emergent properties of brains, linking the discipline to neuroscience. As social scientists, psychologists aim to understand the behavior of individuals and groups.Fernald LD (2008)''Psychology: Six perspectives'' (pp.12–15). Thousand Oaks, CA: Sage Publications.Hockenbury & Hockenbury. Psychology. Worth Publishers, 2010. Ψ (''psi''), the first letter of the Greek word ''psyche'' from which the term psychology is derived (see below), is commonly associated with the science. A professional practitioner or researcher involved in the discipline is called a psychologist. Some psychologists can also be classified as behavioral or cognitive scientists. Some psyc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quantum Mechanics
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, quantum field theory, quantum technology, and quantum information science. Classical physics, the collection of theories that existed before the advent of quantum mechanics, describes many aspects of nature at an ordinary (macroscopic) scale, but is not sufficient for describing them at small (atomic and subatomic) scales. Most theories in classical physics can be derived from quantum mechanics as an approximation valid at large (macroscopic) scale. Quantum mechanics differs from classical physics in that energy, momentum, angular momentum, and other quantities of a bound system are restricted to discrete values ( quantization); objects have characteristics of both particles and waves (wave–particle duality); and there are limits to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Schrödinger Equation
The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. It is a key result in quantum mechanics, and its discovery was a significant landmark in the development of the subject. The equation is named after Erwin Schrödinger, 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 a wave function, the quantum-mechanical characterization of an isolated physical system. The equation can be derived from the fact that the time-evolution operator must be unitary, and must therefore be generated by t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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