PolyAgent/wiki_arabic_en_parallel_20231101 huggingface dataset:
Andre Rawls

Andre Rawls (born December 20, 1991) is an American soccer player who plays as a goalkeeper.
Career
College
Rawls spent his entire college career at Saint Mary's College, including a red-shirted year in 2010. Rawls was named the WCC goalkeeper of the year in 2014 and earned first team all-Far West Region honors by the National Soccer Coaches Association of America. He set a program record for career goals-against average at 0.98 and registered 25 career wins and 17 shut-outs.
Professional
On January 20, 2015, Rawls was selected in the third round (44th overall) of the 2015 MLS SuperDraft by New York City FC. He wasn't picked up by New York City, instead signing with their USL affiliate club Wilmington Hammerheads on April 3, 2015. Rawls made 22 appearances for Wilmington in 2015, posting four clean sheets.
Rawls signed with New York City FC on March 3, 2016. Rawls did not appear for NYCFC in 2016 or 2017. Rawls was loaned to Orange County SC in the USL on March 15, 2018. Rawls made 30 appearances for Orange County, including one in the U.S. Open Cup and three in the USL Cup Playoffs.
Rawls was released by New York City at the end of the 2018 season, but was selected by Colorado Rapids in the 2018 MLS Re-Entry Draft.
On March 6, 2019, Rawls was again loaned to the USL Championship, joining Rapids affiliate Colorado Springs Switchbacks FC. Rawls played 15 matches, posting a 64.6 save percentage and six clean sheets. Rawls signed a two-year contract with the Rapids on Nov. 25, 2019.
Rawls did not appear in 2020, but was on the Rapids bench for Colorado's first two matches of the regular season, as well as Colorado's three matches at the MLS is Back Tournament.
In March 2021, Rawls joined USL Championship club Phoenix Rising FC on loan for the 2021 season.
Following the 2021 season, Colorado declined their contract option on Rawls.
References
External links
Living people
1991 births
American men's soccer players
Soccer players from California
People from San Ramon, California
Sportspeople from Contra Costa County, California
Men's association football goalkeepers
Saint Mary's Gaels men's soccer players
New York City FC draft picks
Wilmington Hammerheads FC players
New York City FC players
Orange County SC players
Colorado Rapids players
Colorado Springs Switchbacks FC players
Phoenix Rising FC players
USL Championship players
لحساسنة (لكوانين)

لحساسنة (لكوانين)
لحساسنة هو دُوَّار يقع بجماعة سيدي أتيجي، إقليم آسفي، جهة مراكش آسفي في المملكة المغربية. ينتمي الدوّار لمشيخة لكوانين التي تضم 25 دوار. يقدر عدد سكانه بـ 132 نسمة حسب الإحصاء الرسمي للسكان والسكنى لسنة 2004.
مراجع
روابط خارجية
البوابة الوطنية للجماعات الترابية
المندوبية السامية للتخطيط
أماكن مأهولة في لكوانين (سيدي أتيجي)
روبرت يو

روبرت يو هو كاتب مسرحي سنغافوري، ولد في 1940.
مراجع
وصلات خارجية
خريجو برنامج الكتابة الدولي
روائيون سنغافوريون
سنغافوريون من أصل صيني
شعراء سنغافوريون
كتاب دراما ومسرح سنغافوريون
كتاب ذكور سنغافوريون
كتاب غير روائيين ذكور
كتاب غير روائيين سنغافوريون
مواليد 1940
دييغو كاريوكا

دييغو كاريوكا هو لاعب كرة قدم برازيلي في مركز الوسط، ولد في 6 فبراير 1998 في نيتيروي في البرازيل. لعب مع شاختيور سوليجورسك وغريميو بورتو أليغرينزي ونادي فيتيبسك.
مراجع
وصلات خارجية
لاعبو كرة قدم رجالية مغتربون في بولندا
لاعبو كرة قدم رجالية مغتربون في أذربيجان
لاعبو كرة قدم رجالية مغتربون في روسيا البيضاء
لاعبو كرة قدم رجالية مغتربون في أوكرانيا
لاعبو كرة قدم رجالية مغتربون في المجر
لاعبو كرة قدم رجالية برازيليون مغتربون
أشخاص على قيد الحياة
رياضيون برازيليون مغتربون في المجر
رياضيون برازيليون مغتربون في أذربيجان
رياضيون برازيليون مغتربون في أوكرانيا
رياضيون برازيليون مغتربون في بولندا
رياضيون برازيليون مغتربون في روسيا البيضاء
رياضيون من نيتيروي
لاعبو البطولة الوطنية المجرية
لاعبو الدوري الأوكراني الممتاز
لاعبو الدوري البولندي الممتاز
لاعبو الدوري البيلاروسي لكرة القدم
لاعبو دوري أذربيجان الممتاز
لاعبو زالايغيرزيغي تورنا إغيليت
لاعبو شاختيور سوليجورسك
لاعبو غريميو بورتو أليغرينزي
لاعبو كرة القدم البرازيليون
لاعبو كرة قدم برازيليون
لاعبو كرة قدم مغتربون برازيليون
لاعبو كرة قدم مغتربون في المجر
لاعبو كرة قدم مغتربون في أوكرانيا
لاعبو كرة قدم مغتربون في بولندا
لاعبو كرة قدم مغتربون في روسيا البيضاء
لاعبو كرة قدم من نيتيروي
لاعبو نادي فيتيبسك
لاعبو نادي لاجيادينزي
لاعبو وسط كرة قدم رجالية
لاعبو ياغيلونيا بياويستوك
مواليد 1998
Pascale Sakr

Pascale Sakr
Pascale Etienne Sakr (born September 23, 1964) is a Lebanese singer. She was born in Zahlé, Lebanon to Maronite parents from Ain Ebel, south of Lebanon. She performs a leading character in many musicals. She graduated from law school in 1987.
Biography
She is also the daughter of Lebanese nationalist Etienne Sakr, a former member of the Lebanese Forces and Leader of the Far-Right Guardians of the Cedars and to Alexandra Sakr. She is the oldest of 3 children and her younger sister is also a Lebanese pop star Karol Sakr. She started singing at a very young age. Her repertoire includes many languages including Lebanese Arabic, French, and English.
Pascale Sakr has also been active in theatre she has starred in lead role of the play Wadi Chamseen and Sawret Chaab.
Personal life
Pascale Sakr is married to Karl Zacca and has two children, Alexander and Annabel.
Discography
Songs
"Sarek Makatibi" Music by Elias Rahbani
"Risho el Fil" Music by Elias Rahbani
"Maoul Music" by Elias Rahbani
"Biddallak Sayfi" Music by Mansour Rahbani
"Ardak el Karami" Music by Antoine Gebara
"Waad Ya Lebnan" Music by Elias Rahbani
"Gharrabou" Music by Melhem Barakat
"Nasheed al Ward" Music by Wajdy Shaya. Lyrics by Anwar Salman
"Oh Babe" By Elias Rahbani
"Sad Is My Story" By Elias Rahbani
"Ya Hami el Hima" By Wajdy Shaya. Lyrics by Hassan Saad
"Yemken By Wajdy Shaya" Lyrics by Anwar Salman
"Am Yenzel el Talj" by Elias Rahbani
"Jayi Papa" Noel by Elias Rahbani
Awards
References
External links
1964 births
Living people
20th-century Lebanese women singers
Lebanese Maronites
People from Zahle
Performers of Christian music in Arabic
روب بوين

روب بوين هو لاعب كرة قاعدة أمريكي، ولد في 24 فبراير 1981 في بيدفورد في الولايات المتحدة.
مراجع
وصلات خارجية
لاعبو كرة قاعدة من مقاطعة تارانت (تكساس)
أشخاص على قيد الحياة
أشخاص من بيدفورد (تكساس)
رياضيون من فورت واين
لاعبو أوكلاند أثلتكس
لاعبو أوكلاند لألعاب القوى
لاعبو روتشستر ريد وينجس
لاعبو سان دييغو بادريس
لاعبو شيكاغو كابز
لاعبو كرة قاعدة من تكساس
لاعبو مينيسوتا توينس
ملتقطو دوري كرة القاعدة الرئيسي
مواليد 1981
لاعبو كرة قاعدة من فورت واين
أدلايد بلو إيغيلز

أدلايد بلو إيغيلز هو نادي كرة قدم أسترالي تم إنشاؤه في سنة 1958 الميلادية
طالع أيضا
دوري الدرجة الأولى الأسترالي
المصادر
أندية كرة قدم أسست في 1958
أندية كرة قدم في أستراليا
أندية كرة قدم في جنوب أستراليا
تأسيسات سنة 1958 في أستراليا
Jessica Cooper

Jessica Cooper (born 1967) is a designer and painter, living in Cornwall, England. She is a Royal West of England Academician and a member of the Newlyn Society of Artists.
Cooper was born in Bristol and grew up in Cornwall. During 1985 and 1986, Cooper did a foundation course at the Falmouth School of Art. At Goldsmiths College from 1986 to 1989 Cooper earned a B.A. (Hons) in Fine Art and Textiles. Cooper coordinated the educational programme for the Newlyn Art Gallery's St. Ives International in 1997. She organised and led the course The Representational to the Abstract at Dartington Hall. Cooper had a solo show at the Newlyn Gallery in 2001 and has featured in several group shows. Her work was featured in the 2007 "Art Now Cornwall" exhibition, at Tate St Ives.
References
External links
Official website
1967 births
Living people
20th-century English women artists
21st-century English women artists
Alumni of Goldsmiths, University of London
Artists from Bristol
British contemporary painters
English women painters
St Ives artists
Daniel C. MacDonald

Daniel C. MacDonald
Daniel Charles MacDonald (1882 – after 1927 — in Boston in old age) was a farmer and political figure on Prince Edward Island. He represented 1st Kings in the Legislative Assembly of Prince Edward Island from 1920 to 1923 as a Liberal.
He was born in Greenvale, Lot 46, Prince Edward Island, the son of Ronald MacDonald. He married Sarah MacDonald. MacDonald was defeated when he ran for reelection in 1923. He lived in Greenvale and moved to Massachusetts sometime before 1927. MacDonald died in Boston.
References
Prince Edward Island Liberal Party MLAs
1882 births
Year of death missing
Canadian emigrants to the United States
Edwin Mansfield

Edwin Mansfield (1930 – 17 November 1997) was a professor of economics at University of Pennsylvania from 1964 and until his death. From 1985 he was also a director of the Center for Economics and Technology.
Edwin Mansfield is best known for his scientific results concerning technological change / diffusion of innovations, and also for his textbooks on microeconomics, managerial economics, and econometrics that were published in millions copies and translated into foreign languages.
References
Diamond, Arthur M., Jr. 2003. "Edwin Mansfield's Contributions to the Economics of Technology," Research Policy, 32(9), pp. 1607-17.
Mansfield, Edwin, et al. 2009. Managerial Economics Theory, Applications, and Cases, 7th Edition. Norton. Contents.
Scherer, F.M. 2005. "Edwin Mansfield: An Appreciation," Essays in Honor of Edwin Mansfield, Part I, Springer, pp.1-7. Abstract.
Teece, David J. 2005. "Technology and Technology Transfer: Mansfieldian Inspirations and Subsequent Developments," Journal of Technology Transfer, 30(1/2), Springer, pp. 17-33. Abstract.
External links
An obituary on the UPENN website
1930 births
1997 deaths
20th-century American economists
Fellows of the Econometric Society
العلاقات المالديفية المالاوية

العلاقات المالديفية المالاوية هي العلاقات الثنائية التي تجمع بين المالديف ومالاوي.
مقارنة بين البلدين
هذه مقارنة عامة ومرجعية للدولتين:
منظمات دولية مشتركة
يشترك البلدان في عضوية مجموعة من المنظمات الدولية، منها:
وصلات خارجية
موقع وزارة الخارجية المالديفية
مراجع
قائمة جزر الفلبين

قائمة جزر الفلبين
تتألف جزر الفلبين (المعروفة أيضًا باسم جزر أرخبيل الفلبين) من حوالي 7641 جزيرة، حوالي 2000 منها فقط مأهولة بالسكان. ولا يزال هناك أكثر من 5000 جزيرة في الأرخبيل لم تُعطى أسماء رسمية بعد.
ترتيب الجزر حسب الحجم
فيما يلي قائمة بأكبر جزر الفلبين. هناك اختلافات طفيفة في تقدير المساحات عبر مصادر مختلفة ، مما قد يغير تصنيف بعض الجزر الأصغر.
تبلغ مساحة أكبر 50 جزيرة مجتمعة حوالي 300000 كيلومتر مربع (120.000 ميل مربع) ويبلغ عدد سكانها مجتمعة حوالي 102 مليون (2015) ؛ وبالتالي فهذه الجزر تشكل حوالي 99 ٪ من إجمالي مساحة الفلبين وإجمالي السكان (2015).
مراجع
أرخبيلات الفلبين
جزر الفلبين
قوائم الجزر حسب البلد
قوائم تضاريس الفلبين
قوائم جزر الفلبين
Priscilla Mensah

Priscilla Mensah (born 19 April 1974) is a Ghanaian footballer who played as a goalkeeper for the Ghana women's national football team. She was part of the team at the 1999 FIFA Women's World Cup. On club level she played for Postal Ladies in Ghana.
References
External links
1974 births
Living people
Ghanaian women's footballers
Ghana women's international footballers
Place of birth missing (living people)
1999 FIFA Women's World Cup players
Women's association football goalkeepers
تروي (توضيح)

تروي (توضيح)
قد تُشير تروي إلى المدينة التاريخية طروادة
أماكن
تروي، أوهايو
تروي، أيداهو
تروي، كارولاينا الشمالية
تروي، ألاباما
صفحات توضيح أسماء أماكن
Oh Won-jong

Oh Won-jong
Oh Won-Jong (born June 17, 1983) is a South Korean football player who plays for Busan TC.
Club career
He joined K-League side Gyeongnam FC in the 2006 draft. In Gyeongnam, he played 4 league games, and 4 league cup games. One year later, he moved to Korea National League side, Gangneung City FC. He played 21 games, scored 4 goals, and made 1 assist for Gangneung. From 2009, Oh played at newly formed Gangwon FC as founding member. On 29 November 2010, he joined Sangju Sangmu FC for military duty. On 3 September 2012, he discharged from military services and returned Gangwon FC.
Club career statistics
References
External links
1983 births
Living people
South Korean men's footballers
Gyeongnam FC players
Gangwon FC players
Gimcheon Sangmu FC players
K League 1 players
Korea National League players
Men's association football midfielders
NGC 1664

NGC 1664 is an open cluster in the constellation of Auriga. It contains stars with a total of around 640 solar masses with a tidal radius of .
NGC 1664 is a somewhat young cluster, with an age of 675 ± 50 Myr, and is dynamically relaxed. It is located some 4,200 light-years away, or about 1.3 kpc. Born outside of the solar circle, it orbits the center of the Milky Way every 244 million years.
References
External links
NGC 1664
NGC 1664
Image NGC 1664
NGC 1664
1664
Auriga (constellation)
فيرال (فيلم)

فيرال (فيلم)
فيرال هو فيلم خيال علمي رعب أمريكي تم إنتاجه في سنة 2016 وهو من إخراج أرييل شلومان و هنري جوست ومن سيناريو كريستوفر لاندون وبربارا مارشال وبطولة صوفيا بلاك ديليا و أنالي تيبتون و ترافيس توب وماشين غان كيلي و ميخائيل كيلي. تم توزيع الفيلم عن طريق شركة ديمينشن فيلمز.
القصة
تتكلم قصة الفيلم عن أختين ستايسي وإيما في المرحلة الإعدادية ينتقلان إلى بلدة في كاليفورنيا، وتكونان صداقات في مدرستهن الجديدة، لكنهن تكتشفان وجود دماء في المدرسة وسلوك غريب فيها، ليكتشفوا بأنه مرض غريب أصاب المنطقة.
البطولة
صوفيا بلاك ديليا بدور إيما دراكفورد
أنالي تيبتون بدور ستايسي دراكفورد
ترافيس توب بدور إيفان كلاين
ماشين غان كيلي بدور سي جاي (كولسون بيكر)
ميخائيل كيلي بدور مايكل دراكفورد
جون كوثران بدور جونيور تومي
ستوني ويستمورلاند بدور بيل
لينزي غراي بدور غريسي ليماي
جودين إلدر بدور السيدة تومي
فيليب ليبس بدور غانغلي كيد
براين هوي بدور تارا دانلي
التقييم
لم يحصل الفيلم على إيرادات عالية. في موقع الطماطم الفاسدة حصل الفيلم على تقييم 54% بناءً على 13 مراجعة.
مراجع
وصلات خارجية
فيرال على قاعدة بيانات الأفلام على الإنترنت
أفلام أمريكية
أفلام أمريكية في عقد 2010
أفلام إثارة خيال علمي أمريكية
أفلام إثارة خيال علمي عقد 2010
أفلام إثارة رعب أمريكية
أفلام إنتاج 2016
أفلام باللغة الإنجليزية
أفلام باللغة الإنجليزية في عقد 2010
أفلام بلومهاوس برودكشن
أفلام خيال علمي رعب أمريكية
أفلام خيال علمي رعب عقد 2010
أفلام ديمينجن فيلمز
أفلام رعب إثارة 2016
أفلام رعب في 2016
أفلام رعب ومراهقة أمريكية
أفلام زومبي أمريكية
أفلام عن تفشي الفيروسات
أفلام من إنتاج جايسون بلوم
محمد السقاف (لاعب كرة قدم)

محمد السقاف (لاعب كرة قدم)
محمد السقاف (ولد في 19 أكتوبر 2000) هو لاعب كرة قدم سعودي لعب سابقاً في نادي المجزل.
مراجع
أشخاص على قيد الحياة
لاعبو دوري الدرجة الثانية السعودي
لاعبو كرة قدم سعوديون
لاعبو نادي المجزل
مواليد 2000
دوموس دي ماريا

دوموس دي ماريا ، ، (سردينيا: )، هي بلدية في مقاطعة جنوب سردينيا، في المنطقة الإيطالية سردينيا، وتقع على بعد حوالي 35 كيلومترا (22 ميل) جنوب غرب كالياري.
السكان
في سنة 1861 بلغ عدد السكان نسمة، وتطور العدد ليصل في سنة 2011 لـ نسمة.
مراجع
Dan Weinstein (speed skater)

Dan Weinstein (speed skater)
Daniel Weinstein (born February 4, 1981) is a retired American short track speed skating competitor and two-time Olympian.
Biography
Of the handful of Jewish-American Olympians who competed in the 1998 Winter Olympics at Nagano, Japan, Weinstein was by far the youngest. At 17 years of age, he was not only the youngest athlete on the U.S. speedskating team, he was also the youngest man on the entire U.S. Winter Olympics Team. Four years later, Weinstein competed in the 2002 Winter Olympics in Salt Lake City, Utah.
Weinstein has won multiple individual distance US Championships, and he won the men's overall title at the 2000 U.S. Short Track Speedskating Championships.
In 1994, Weinstein was the youngest person to ever skate in the Olympic trials, but he placed poorly.
Raised in Brookline, Massachusetts, he began skating at age eight, after his parents saw an article about local speedskating in the Boston Globe.
He completed his bachelor's degree at Harvard University in 2004, and his MBA at The Tuck School of Business at Dartmouth in 2009.
See also
List of select Jewish speed skaters
References
Sources
Jewish Sports profile
Dan Weinstein '03: Go Speed Racer Go, Harvard Crimson, March 2, 2000 (via Google Cache)
Dan Weinstein at ISU
Dan Weinstein at the-sports.org
1981 births
Living people
American male short track speed skaters
Olympic short track speed skaters for the United States
Short track speed skaters at the 1998 Winter Olympics
Short track speed skaters at the 2002 Winter Olympics
Sportspeople from Brookline, Massachusetts
Harvard University alumni
Jewish American sportspeople
American male speed skaters
Tuck School of Business alumni
21st-century American Jews
Cosmas I of Alexandria

Cosmas I of Alexandria
Cosmas I or Kosmas I served as Greek Patriarch of Alexandria between and his death in 768.
Cosmas was the first residential Chalcedonian (Melkite) patriarch to be established in Alexandria following the Muslim conquest of Egypt in the 640s. The see had remained vacant since, but Cosmas was appointed with the consent of both the Umayyad Caliph and the Byzantine Emperor. The chronicler Theophanes the Confessor reports that in 742/3, he abjured Monotheletism, the dominant doctrine among Alexandrian Melkites since it had been promulgated by Emperor Heraclius. As Cosmas himself was most likely not a Monothelete, this has been interpreted by modern scholarship as a garbled reference to Alexandria's recognition by the other Chalcedonian patriarchates.
References
Sources
768 deaths
8th-century Patriarchs of Alexandria
8th-century people from the Abbasid Caliphate
Christians from the Umayyad Caliphate
8th-century people from the Umayyad Caliphate
Clyde Frederick Shannon Jr.

Clyde Frederick Shannon Jr. (born 1942) is a former United States district judge of the United States District Court for the Western District of Texas.
Education and career
Born in Marshall, Texas, Shannon received a Bachelor of Business Administration from Loyola University New Orleans in 1965 and a Bachelor of Laws from the University of Texas School of Law in 1968. He was in private practice in San Antonio, Texas from 1968 to 1975. He was a judge of the 131st District Court of Texas from 1975 to 1980.
Federal judicial service
Shannon was nominated by President Jimmy Carter on December 19, 1979, to a seat on the United States District Court for the Western District of Texas vacated by Judge Dorwin Wallace Suttle. He was confirmed by the United States Senate on June 18, 1980, and received his commission the same day. Shannon served until his resignation on January 1, 1984.
Post judicial service
Shannon returned to the private practice of law in San Antonio following his resignation from the federal bench.
References
Sources
1942 births
Living people
Judges of the United States District Court for the Western District of Texas
Loyola University New Orleans alumni
People from Marshall, Texas
United States district court judges appointed by Jimmy Carter
20th-century American judges
University of Texas School of Law alumni
Albert Weinstein

Albert Weinstein
Georg Albert Weinstein (October 13, 1885 – December 7, 1969) was a German track and field athlete who competed in the 1908 Summer Olympics. In 1908 he finished sixth, seventh, or possibly 8th in the long jump competition.
References
External links
list of German athletes
1885 births
1969 deaths
German male long jumpers
Olympic athletes for Germany
Athletes (track and field) at the 1908 Summer Olympics
Alfredo Ramos (Brazilian footballer)

Alfredo Ramos (Brazilian footballer)
Alfredo Ramos de Oliveira (27 October 1924 in Jacareí – 31 July 2012), was a Brazilian footballer in the defense role. He was simply known as Alfredo or Polvo by fans.
In his career as player for Santos (1947–1951), São Paulo (1951–1958 and 1961) and Corinthians (1958–1960), he played 633 games, scoring 3 goals, and won one São Paulo State Championship in 1953. With the Brazilian team, he was in the first team in 10 games and was listed in the roster for the 1954 FIFA World Cup, without playing any games. In the 1970s, he was coach for the São Paulo squad (see List of São Paulo Futebol Clube managers).
Honours
São Paulo
Campeonato Paulista: 1953, 1957
References
1924 births
2012 deaths
People from Jacareí
Brazilian men's footballers
Brazilian football managers
Campeonato Brasileiro Série A players
1954 FIFA World Cup players
Campeonato Brasileiro Série A managers
Brazil men's international footballers
Clube Atlético Juventus players
Santos FC players
São Paulo FC players
Sport Club Corinthians Paulista players
São Paulo state football team players
São Paulo FC managers
Sport Club Corinthians Paulista managers
Men's association football defenders
Footballers from São Paulo (state)
Energy operator

Energy operator
In quantum mechanics, energy is defined in terms of the energy operator, acting on the wave function of the system as a consequence of time translation symmetry.
Definition
It is given by:
It acts on the wave function (the probability amplitude for different configurations of the system)
Application
The energy operator corresponds to the full energy of a system. The Schrödinger equation describes the space- and time-dependence of the slow changing (non-relativistic) wave function of a quantum system. The solution of this equation for a bound system is discrete (a set of permitted states, each characterized by an energy level) which results in the concept of quanta.
Schrödinger equation
Using the energy operator to the Schrödinger equation:
can be obtained:
where i is the imaginary unit, ħ is the reduced Planck constant, and is the Hamiltonian operator.
Constant energy
Working from the definition, a partial solution for a wavefunction of a particle with a constant energy can be constructed. If the wavefunction is assumed to be separable, then the time dependence can be stated as , where E is the constant energy. In full,
where is the partial solution of the wavefunction dependent on position. Applying the energy operator, we have
This is also known as the stationary state, and can be used to analyse the time-independent Schrödinger equation:
where E is an eigenvalue of energy.
Klein–Gordon equation
The relativistic mass-energy relation:
where again E = total energy, p = total 3-momentum of the particle, m = invariant mass, and c = speed of light, can similarly yield the Klein–Gordon equation:
where is the momentum operator. That is:
Derivation
The energy operator is easily derived from using the free particle wave function (plane wave solution to Schrödinger's equation). Starting in one dimension the wave function is
The time derivative of is
By the De Broglie relation:
we have
Re-arranging the equation leads to
where the energy factor E is a scalar value, the energy the particle has and the value that is measured. The partial derivative is a linear operator so this expression is the operator for energy:
It can be concluded that the scalar E is the eigenvalue of the operator, while is the operator. Summarizing these results:
For a 3-d plane wave
the derivation is exactly identical, as no change is made to the term including time and therefore the time derivative. Since the operator is linear, they are valid for any linear combination of plane waves, and so they can act on any wave function without affecting the properties of the wave function or operators. Hence this must be true for any wave function. It turns out to work even in relativistic quantum mechanics, such as the Klein–Gordon equation above.
See also
Time translation symmetry
Planck constant
Schrödinger equation
Momentum operator
Hamiltonian (quantum mechanics)
Conservation of energy
Complex number
Stationary state
References
Energy
Partial differential equations
Quantum mechanics