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The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. 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href="http://dbpedia.org/resource/Probability_amplitude">Probability amplitude</a> </h1> </div> </div> <div class="row"> <div class="col"> <div class="text-muted"> An Entity of Type: <a href="http://dbpedia.org/class/yago/Abstraction100002137">Abstraction100002137</a>, from Named Graph: <a href="http://dbpedia.org">http://dbpedia.org</a>, within Data Space: <a href="http://dbpedia.org">dbpedia.org</a> </div> </div> </div> <div class="row pt-2"> <div class="col-xs-9 col-sm-10"> In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Ph </div> <div class="col-xs-3 col-sm-2"> <a href="#" class="thumbnail"> <img src="http://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300" alt="thumbnail" class="img-fluid" /> </a> </div> </div> </div> </section>   <section> <div class="container-xl"> <div class="row"> <div class="table-responsive"> <table class="table table-hover table-sm table-light"> <thead> <tr> <th class="col-xs-3 ">Property</th> <th class="col-xs-9 px-3">Value</th> </tr> </thead> <tbody> <tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/abstract">dbo:abstract</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">سعة الاحتمال في ميكانيكا الكم هو عدد مركب يعطى مربع قيمته المطلقة احتمال وجود جسيم في نقطة ما في الفراغ طبقاً لأحد حلول دالة موجية. وعلى سبيل المثال فقيم دالة موجية موحدة تمثل بعدد من السعات (مطالات) حيث أن تعطي كثافة احتمال التواجد في النقطة {x}. وقد تؤدي سعة الاحتمال أيضا إلى حلول ذات قيم متقطعة للدالة الموجية. بافتراض حالة جسيم كمومي، وطبقا لتفسير كوبنهاغن فإن قيم الدالة الموجية تمثل مطالات احتمال التواجد في نقطة معينة. فعند تعيين مكان تواجد جسيم فيكون احتمال وجود الجسيم في الحجم مساويا: أي أن يمثل كثافة احتمال وجود الجسيم فيه. (ar)</li> <li style="display:none;">Amplituda pravděpodobnosti je v kvantové mechanice komplexní číslo přiřazené neurčitému nebo neznámému procesu nebo veličině. Pravděpodobnost, že daný proces nastane, je pak udána jako kvadrát (druhá mocnina) absolutní hodnoty amplitudy pravděpodobnosti. Amplitudu pravděpodobnosti nelze přímo měřit. (cs)</li> <li style="display:none;">En mecánica cuántica, la amplitud de probabilidad es un número complejo utilizado para describir el comportamiento sistemas. El cuadrado del módulo de esta cantidad representa una probabilidad o densidad de probabilidad. Las amplitudes de probabilidad proporcionan una relación entre la función de onda (o, más generalmente, de un vector de estado cuántico) de un sistema y los resultados de las observaciones de aquel sistema, una primera relación fue propuesto por Max Born. La interpretación de los valores de una función de onda como la amplitud de probabilidad es un pilar de la interpretación de Copenhague de la mecánica cuántica. De hecho, las propiedades del espacio de las funciones de onda fueron usadas para hacer predicciones físicas (tales como ciertas emisiones de energía discreta por parte de los átomos) antes de cualquier interpretación física de una función particular fuese ofrecida. Born fue premiado en 1954 con el premio Nóbel de Física por esta explicación, así la probabilidad así calculada es a veces llamada la "probabilidad de Born". Estos conceptos probabilistas, concretamente la densidad de probabilidad y las medidas cuánticas, fueron enérgicamente disputadas en el tiempo que los físicos originales que trabajan en teoría, como Schrödinger[la aclaración necesitada] y Einstein. Es la fuente de las consecuencias misteriosas y dificultades filosóficas en las interpretaciones de la de mecánica cuántica- temas que continúan siendo debatidos incluso hoy. Ejemplo: Un qubit puede expresarse como una combinación lineal de los dos estados básicos |ψ⟩ = α |0⟩ + β |1⟩ donde α y β son las amplitudes de probabilidad complejas. La posibilidad de que llegar a un estado de qubit |0⟩ es |α|2 y que tu condición |1⟩ es |β|2, porque se aplica |α|2 + |β|2 = 1 (es)</li> <li style="display:none;">En mécanique quantique, une amplitude de probabilité est un nombre complexe utilisé pour décrire le comportement d'un système. Le carré de son module donne la probabilité (ou la densité de probabilité) pour que le système soit mesuré dans un état donné. (fr)</li> <li>In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Physics for this understanding, and the probability thus calculated is sometimes called the "Born probability". These probabilistic concepts, namely the probability density and quantum measurements, were vigorously contested at the time by the original physicists working on the theory, such as Schrödinger and Einstein. It is the source of the mysterious consequences and philosophical difficulties in the interpretations of quantum mechanics—topics that continue to be debated even today. (en)</li> <li style="display:none;">확률 진폭(確率振幅, 영어: probability amplitude)은 양자역학에서 절댓값의 제곱이 확률 밀도인 복소수 스칼라 물리량이다. 3차원 공간에서 한 입자를 나타내는 파동 함수의 경우 그 단위는 m−3/2이나, 다른 차원에서는 그 단위가 달라진다. 비상대론적 양자역학에서는 공간 기저에서의 파동 함수 가 확률 진폭을 나타낸다. 이런 확률적인 해석이 가능하려면, 파동 함수는 함수 (그 절댓값의 제곱의 적분이 유한한 함수)이어야 한다. (ko)</li> <li style="display:none;">In meccanica quantistica, l'ampiezza di probabilità è una funzione complessa il cui modulo quadro rappresenta la funzione densità di probabilità. Ad ogni particella è associata una ampiezza di probabilità che descrive la sua posizione, in accordo con il principio di indeterminazione di Heisenberg: essa coincide con la funzione d'onda in tal punto. Per una funzione d'onda ψ la funzione di densità di probabilità associata è ψ*ψ, che equivale a |ψ|2. Questa è talvolta definita semplicemente densità di probabilità e può essere normalizzata o non normalizzata. (it)</li> <li style="display:none;">De waarschijnlijkheidsamplitude is in de kwantummechanica een complex getal waarvan het kwadraat van de modulus de kansdichtheid weergeeft dat men het systeem (bij een meting) in een bepaalde toestand aantreft. In de klassieke mechanica is een meetproces eenduidig: als antwoord krijgt men de waarde van de grootheid die men meet. In de kwantummechanica is de uitkomst van een meting echter statistisch van aard. Het is precies dit statistisch karakter dat wordt uitgedrukt door de waarschijnlijkheidsamplitude. Voor een systeem met golffunctie wordt de kansdichtheid gegeven door (het kwadraat van de modulus van de golffunctie). Voor een systeem met golffunctie is de kansdichtheid gelijk aan: = , waarbij Ψ(x)* de complex geconjugeerde is van de golffunctie Ψ(x). De kans om een deeltje (op de x-as) in het interval a,b aan te treffen is gelijk aan de integraal van de kansdichtheid, gegeven de grenzen x = a en x = b. Het verband tussen waarschijnlijkheidsdichtheden en golffuncties werd voor het eerst gelegd door de Duitse fysicus Max Born (1882 - 1970) met de zogeheten Born-regel. (nl)</li> <li style="display:none;">Основные положения статистической интерпретации волновой функции были сформулированы Максом Борном в 1926 году, как только было опубликовано волновое уравнение Шрёдингера. В отличие от интерпретации Шрёдингера, представляющей электрон в атоме в виде волнового пакета, интерпретация Борна рассматривала электрон в атоме как отрицательно заряженную элементарную частицу и сохраняла структуру электрона. Но при этом законы движения электрона в атоме приобретают вероятностный характер, определяемый волновой функцией. В рамках статистической интерпретации волновой функции терялся смысл понятия траектории движения электрона, однако можно было рассматривать вероятность нахождения электрона в определённом элементе пространства, окружающего ядро атома. М. Борн вспоминал: Он (Шрёдингер) рассматривал электрон не как частицу, но как некоторое распределение плотности, которое давалось квадратом его волновой функции |ψ|². Он считал, что следует полностью отказаться от идеи частиц и квантовых скачков, и никогда не сомневался в правильности этого убеждения. Я, напротив, имел возможность каждодневно убеждаться в плодотворности концепции частиц, наблюдая за блестящими опытами Франка по атомным и молекулярным столкновениям, и был убеждён, что частицы не могут быть упразднены. Следовало найти путь к объединению частиц и волн. Я видел связующее звено в идее вероятности… Точку зрения М. Борна разделяли А. Зоммерфельд, Н. Бор, В. Гейзенберг, В. Паули. В 1927 году Н. Бор и В. Гейзенберг усовершенствовали вероятностную интерпретацию волновой функции, данную М. Борном, и попытались ответить на ряд вопросов, возникающих вследствие свойственного квантовомеханического корпускулярно-волнового дуализма (копенгагенская интерпретация). В 1927 году В. Гейзенберг, используя вероятностную трактовку квантовой механики, формулирует соотношение неопределённостей. Принцип неопределённости Гейзенберга становится одним из краеугольных камней квантовой механики. Однако сам автор волнового уравнения продолжал настаивать на волновой природе электрона и продолжал рассматривать электрон в атоме как отрицательно заряженное облако. В июне 1927 года аспиранты Шрёдингера В. Гайтлер и Ф. Лондон решили задачу о природе гомеополярной связи в молекуле водорода. Метод Гайтлера — Лондона получил название теории валентных связей. По этому методу считалось, что электронное облако молекулы усиливается в пространстве между ядрами благодаря интерферометрическому наложению исходных атомных орбиталей, что оказывает притягивающее действие на атомы и приводит к образованию ковалентной связи. Завязалась острая многолетняя (четверть века) дискуссия — в чём же заключается сущность шрёдингеровских волн? Что именно колеблется в пространстве, окружающем ядро атома водорода? Чем является электрон в атоме — волновым пакетом или элементарной частицей? Лишь только в 1950 г. Шрёдингер присоединился к вероятностной трактовке сущности волн. Он писал в статье «Что такое элементарная частица»: Волны, о которых мы говорили, не должны считаться реальными волнами. Верно, что они порождают интерференционные явления, которые в случае света, где они уже давно известны, считались решающим доказательством, устранившим любые сомнения в реальности световых волн. Тем не менее, мы теперь говорим, что все волны, включая световые, лучше рассматривать как «волны вероятности». Они являются лишь математическим построением для вычисления вероятности нахождения частицы… В 1954 году М. Борн удостоен Нобелевской премии по физике с формулировкой «За фундаментальное исследование в области квантовой механики, особенно за статистическую интерпретацию волновой функции». (ru)</li> <li style="display:none;">Амплітуда ймовірності — комплексна величина, квадрат модуля якої задає густину ймовірності. Зокрема, у квантовій механіці хвильова функція ψ є амлітудою ймовірності перебування квантовомеханічної системи в певній точці координатного простору. Відповідно, при розкладі хвильової функції в певному ортонормованому базисі , коефіцієнти задають амплітуду ймовірності знайти систему у стані . (uk)</li> <li style="display:none;">Em mecânica quântica, uma amplitude de probabilidade é um número complexo cujo módulo ao quadrado representa uma probabilidade ou densidade de probabilidade. Por exemplo, os valores tirados por uma função de onda normalizada ψ são amplitudes, uma vez que |ψ(x)|² dá a densidade de probabilidade na posição x. Amplitudes de probabilidade podem também corresponderem a probabilidades de resultados discretos. Foi uma hipótese apresentada pelo físico alemão Max Born, em julho de 1926. (pt)</li> <li style="display:none;">的在量子力學裏，機率幅，又稱為量子幅（英語：Probability amplitude），是一個描述量子行為的複數量。事實上是表示初始量子態（）和終末量子態的兩個希爾伯特向量的內積（）；而這個機率幅的絕對值平方就是與從狀態躍遷到狀態的機率： (zh)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/thumbnail">dbo:thumbnail</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:thumbnail" resource="http://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300" href="http://commons.wikimedia.org/wiki/Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300">wiki-commons:Special:FilePath/Hydrogen_eigenstate_n5_l2_m1.png?width=300</a></li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://dbpedia.org/ontology/wikiPageExternalLink">dbo:wikiPageExternalLink</a> </td><td class="col-10 text-break"><ul> <li><a class="uri" rel="dbo:wikiPageExternalLink nofollow" resource="https://feynmanlectures.caltech.edu/III_03.html" 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For which particles? 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resource="http://dbpedia.org/class/yago/Idea105833840" href="http://dbpedia.org/class/yago/Idea105833840">yago:Idea105833840</a></li> <li><a class="uri" rel="rdf:type" resource="http://dbpedia.org/class/yago/PsychologicalFeature100023100" href="http://dbpedia.org/class/yago/PsychologicalFeature100023100">yago:PsychologicalFeature100023100</a></li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#comment">rdfs:comment</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">سعة الاحتمال في ميكانيكا الكم هو عدد مركب يعطى مربع قيمته المطلقة احتمال وجود جسيم في نقطة ما في الفراغ طبقاً لأحد حلول دالة موجية. وعلى سبيل المثال فقيم دالة موجية موحدة تمثل بعدد من السعات (مطالات) حيث أن تعطي كثافة احتمال التواجد في النقطة {x}. وقد تؤدي سعة الاحتمال أيضا إلى حلول ذات قيم متقطعة للدالة الموجية. بافتراض حالة جسيم كمومي، وطبقا لتفسير كوبنهاغن فإن قيم الدالة الموجية تمثل مطالات احتمال التواجد في نقطة معينة. فعند تعيين مكان تواجد جسيم فيكون احتمال وجود الجسيم في الحجم مساويا: أي أن يمثل كثافة احتمال وجود الجسيم فيه. (ar)</li> <li style="display:none;">Amplituda pravděpodobnosti je v kvantové mechanice komplexní číslo přiřazené neurčitému nebo neznámému procesu nebo veličině. Pravděpodobnost, že daný proces nastane, je pak udána jako kvadrát (druhá mocnina) absolutní hodnoty amplitudy pravděpodobnosti. Amplitudu pravděpodobnosti nelze přímo měřit. (cs)</li> <li style="display:none;">En mécanique quantique, une amplitude de probabilité est un nombre complexe utilisé pour décrire le comportement d'un système. Le carré de son module donne la probabilité (ou la densité de probabilité) pour que le système soit mesuré dans un état donné. (fr)</li> <li style="display:none;">확률 진폭(確率振幅, 영어: probability amplitude)은 양자역학에서 절댓값의 제곱이 확률 밀도인 복소수 스칼라 물리량이다. 3차원 공간에서 한 입자를 나타내는 파동 함수의 경우 그 단위는 m−3/2이나, 다른 차원에서는 그 단위가 달라진다. 비상대론적 양자역학에서는 공간 기저에서의 파동 함수 가 확률 진폭을 나타낸다. 이런 확률적인 해석이 가능하려면, 파동 함수는 함수 (그 절댓값의 제곱의 적분이 유한한 함수)이어야 한다. (ko)</li> <li style="display:none;">In meccanica quantistica, l'ampiezza di probabilità è una funzione complessa il cui modulo quadro rappresenta la funzione densità di probabilità. Ad ogni particella è associata una ampiezza di probabilità che descrive la sua posizione, in accordo con il principio di indeterminazione di Heisenberg: essa coincide con la funzione d'onda in tal punto. Per una funzione d'onda ψ la funzione di densità di probabilità associata è ψ*ψ, che equivale a |ψ|2. Questa è talvolta definita semplicemente densità di probabilità e può essere normalizzata o non normalizzata. (it)</li> <li style="display:none;">Амплітуда ймовірності — комплексна величина, квадрат модуля якої задає густину ймовірності. Зокрема, у квантовій механіці хвильова функція ψ є амлітудою ймовірності перебування квантовомеханічної системи в певній точці координатного простору. Відповідно, при розкладі хвильової функції в певному ортонормованому базисі , коефіцієнти задають амплітуду ймовірності знайти систему у стані . (uk)</li> <li style="display:none;">Em mecânica quântica, uma amplitude de probabilidade é um número complexo cujo módulo ao quadrado representa uma probabilidade ou densidade de probabilidade. Por exemplo, os valores tirados por uma função de onda normalizada ψ são amplitudes, uma vez que |ψ(x)|² dá a densidade de probabilidade na posição x. Amplitudes de probabilidade podem também corresponderem a probabilidades de resultados discretos. Foi uma hipótese apresentada pelo físico alemão Max Born, em julho de 1926. (pt)</li> <li style="display:none;">的在量子力學裏，機率幅，又稱為量子幅（英語：Probability amplitude），是一個描述量子行為的複數量。事實上是表示初始量子態（）和終末量子態的兩個希爾伯特向量的內積（）；而這個機率幅的絕對值平方就是與從狀態躍遷到狀態的機率： (zh)</li> <li style="display:none;">En mecánica cuántica, la amplitud de probabilidad es un número complejo utilizado para describir el comportamiento sistemas. El cuadrado del módulo de esta cantidad representa una probabilidad o densidad de probabilidad. Es la fuente de las consecuencias misteriosas y dificultades filosóficas en las interpretaciones de la de mecánica cuántica- temas que continúan siendo debatidos incluso hoy. Ejemplo: Un qubit puede expresarse como una combinación lineal de los dos estados básicos |ψ⟩ = α |0⟩ + β |1⟩ |α|2 + |β|2 = 1 (es)</li> <li>In quantum mechanics, a probability amplitude is a complex number used for describing the behaviour of systems. The modulus squared of this quantity represents a probability density. Probability amplitudes provide a relationship between the quantum state vector of a system and the results of observations of that system, a link was first proposed by Max Born, in 1926. Interpretation of values of a wave function as the probability amplitude is a pillar of the Copenhagen interpretation of quantum mechanics. In fact, the properties of the space of wave functions were being used to make physical predictions (such as emissions from atoms being at certain discrete energies) before any physical interpretation of a particular function was offered. Born was awarded half of the 1954 Nobel Prize in Ph (en)</li> <li style="display:none;">De waarschijnlijkheidsamplitude is in de kwantummechanica een complex getal waarvan het kwadraat van de modulus de kansdichtheid weergeeft dat men het systeem (bij een meting) in een bepaalde toestand aantreft. In de klassieke mechanica is een meetproces eenduidig: als antwoord krijgt men de waarde van de grootheid die men meet. In de kwantummechanica is de uitkomst van een meting echter statistisch van aard. Het is precies dit statistisch karakter dat wordt uitgedrukt door de waarschijnlijkheidsamplitude. Voor een systeem met golffunctie wordt de kansdichtheid gegeven door (het kwadraat van de modulus van de golffunctie). (nl)</li> <li style="display:none;">Основные положения статистической интерпретации волновой функции были сформулированы Максом Борном в 1926 году, как только было опубликовано волновое уравнение Шрёдингера. В отличие от интерпретации Шрёдингера, представляющей электрон в атоме в виде волнового пакета, интерпретация Борна рассматривала электрон в атоме как отрицательно заряженную элементарную частицу и сохраняла структуру электрона. Но при этом законы движения электрона в атоме приобретают вероятностный характер, определяемый волновой функцией. В рамках статистической интерпретации волновой функции терялся смысл понятия траектории движения электрона, однако можно было рассматривать вероятность нахождения электрона в определённом элементе пространства, окружающего ядро атома. (ru)</li> </ul></td></tr><tr class="odd"><td class="col-2"><a class="uri" href="http://www.w3.org/2000/01/rdf-schema#label">rdfs:label</a> </td><td class="col-10 text-break"><ul> <li style="display:none;">سعة الاحتمال (ar)</li> <li style="display:none;">Amplituda pravděpodobnosti (cs)</li> <li style="display:none;">Amplitud de probabilidad (es)</li> <li style="display:none;">Ampiezza di probabilità (it)</li> <li style="display:none;">Amplitude de probabilité (fr)</li> <li style="display:none;">확률 진폭 (ko)</li> <li style="display:none;">Waarschijnlijkheidsamplitude (nl)</li> <li>Probability amplitude (en)</li> <li style="display:none;">Amplitude de probabilidade (pt)</li> <li style="display:none;">Статистическая интерпретация волновой функции (ru)</li> <li style="display:none;">機率幅 (zh)</li> <li style="display:none;">Амплітуда ймовірності (uk)</li> </ul></td></tr><tr class="even"><td class="col-2"><a class="uri" href="http://www.w3.org/2002/07/owl#sameAs">owl:sameAs</a> </td><td 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