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Bra-ket notation was designed to facilitate the formal manipulation of linear-algebraic expressions.
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Bra-ket and notation
In quantum mechanics, Bra-ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars.
Bra-ket notation is widespread in quantum mechanics: almost every phenomenon that is explained using quantum mechanics — including a large portion of modern physics — is usually explained with the help of bra-ket notation.
Bra-ket notation uses a specific notation for inner products:
Bra-ket notation splits this inner product ( also called a " bracket ") into two pieces, the " bra " and the " ket ":
Bra-ket notation can be used even if the vector space is not a Hilbert space.
Bra-ket notation makes it particularly easy to compute the Hermitian conjugate ( also called dagger, and denoted †) of expressions.
* Bra-ket notation for outer product
** Bra-ket notation can be used to manipulate wave functions.
Note the use of Bra-ket notation.
* Bra-ket notation
* Bra-ket notation or Dirac Notation is another representation of probability in quantum mechanics
# REDIRECT Bra-ket notation
** Bra-ket notation
* Bra-ket notation
In quantum computing, the cat state, named after Schrödinger's cat, is the special quantum state where the qubits are in an equal superposition of all being | 0 > and all being | 1 >, i. e. ( in Bra-ket notation ): | 00 ... 0 > +| 11 ... 1 >.
notation and was
The notation was introduced by Karl Weierstrass in 1841.
The system was revolutionary by including a zero and positional notation.
The decimal point notation was introduced by Sind ibn Ali, he also wrote the earliest treatise on Arabic numerals.
The notation was introduced in 1939 by Paul Dirac and is also known as Dirac notation, though the notation has precursors in Grassmann's use of the notation for his inner products nearly 100 years previously.
The notation was introduced by Andreas von Ettingshausen in 1826, although the numbers were already known centuries before that ( see Pascal's triangle ).
Here, the idea was to map mathematical notation to a natural number ( using a Gödel numbering ).
The current system of chemical notation was invented by Berzelius.
because it does not explicitly make use of religious titles for Jesus, such as " Christ " and Domin-(" Lord "), which are used in the BC / AD notation, nor does it give implicit expression to the Christian creed that Jesus was the Christ.
In some communist states during the Cold War period, usage of non-religious notation was mandated.
Although Xenakis could well have composed this music by hand, the intensity of the calculations needed to transform probabilistic mathematics into musical notation was best left to the number-crunching power of the computer.
While his system was less " scientific " than that of J. P. Lesley, it's other key features – notation, specificity, and versatility – make it deserving of the praise it has received.
There was a notation in use like ' tenth-metre ', meaning the tenth decimal of the metre, currently an Angstrom.
The example above shows a notation named " type-image-svg " that references the standard public FPI and the system identifier ( the standard URI ) of an SVG 1. 1 document, instead of specifying just a system identifier as in the first example ( which was a relative URI interpreted locally as a MIME type ).
Other notational traditions do exist ; Italian solo music is typically written at the sounding pitch, and the " old " German method sounded an octave below where notation except in the treble clef, where the music was written at pitch.
He was the first person to use algebraic notation and symbolism.
Some of the limitations of Diophantus ' notation are that he only had notation for one unknown and, when problems involved more than a single unknown, Diophantus was reduced to expressing " first unknown ", " second unknown ", etc.
Western musical notation was originally created to preserve the lines of Gregorian chant, which before its invention was taught as an oral tradition in monastic communities.
The only element lacking for the creation of these fields was an efficient algebraic notation in which to express his concepts.
His notation for the cardinal numbers was the Hebrew letter ( aleph ) with a natural number subscript ; for the ordinals he employed the Greek letter ω ( omega ).
notation and designed
In the 1960s linguist William Stokoe created the first writing system for a sign language, the so-called Stokoe notation, which he designed specifically for ASL.
Scorewriting, or notation software typically lacks advanced sequencing tools, and is optimized for the creation of a neat, professional printout designed for live instrumentalists.
It is also designed to be easy to read by people, and many musicians learn to read it directly instead of using a computer program to transform it into a standard musical notation score.
Hungarian notation was designed to be language-independent, and found its first major use with the BCPL programming language.
Because of the way its processor ( a custom chip from Texas Instruments ) is designed, it relies on reverse Polish notation ( RPN ).
* The third current implementation is ProofPower a collection of tools designed to provide special support for working with the Z notation for formal specification.
Shape notes are a music notation designed to facilitate congregational and community singing.
In iconic phonetic notation, the shapes of the phonetic characters are designed so that they visually represent the position of articulators in the vocal tract.
The multi-line format was designed to permit writing of HAL / S code that is similar to mathematical notation.
In 1960, Łukasiewicz notation concepts and stacks were used as the basis of the Burroughs B5000 computer designed by Robert S. Barton and his team at Burroughs Corporation in Pasadena, California.
The suite of games is designed to teach the principles of symbolic logic to children ( in Polish notation ).
However, as this format was designed for playback ( e. g. by sequencers ) rather than notation, it only produces approximate results and much notational information is lost in the process
It made the 5100 appear the same as an IBM 2741 Communications Terminal and was designed to be able to communicate with IBM 2741 compatible machines in start-stop mode using the EBCD ( Extended Binary Coded Decimal ) notation.
Making use of abstract symbols Action Stroke Dance Notation is visually similar to Motif notation, a subset of Labannotation that is also designed for speed of writing.
Although braille notation was designed for people who are blind or visually impaired to read, prior to the introduction of the Perkins Brailler, writing braille was a cumbersome process.
Shape notes are a system of music notation designed to facilitate choral singing.
* Smith notation is a straightforward chess notation designed to be reversible and represent any move without ambiguity.
Byzantine chant manuscripts date from the 9th century, while lectionaries of biblical readings in Ekphonetic notation ( a primitive graphic system designed to indicate the manner of reciting lessons from Scripture ) begin about a century earlier and continue in use until the 12th or 13th century.
Fraser also designed a written musical notation for transcribing the Lisu's oral history songs.
The music is intentionally written to be funny, being liberally sprinkled with obtrusively clumsy, mechanical and over-repetitive composition, together with passages evidently designed to mimic the effects of inaccurate notation and inept performance.
They are designed to solve classical algebra equations and problems in human readable notation.
Structured Analysis and Design Technique ( SADT ) is a diagrammatic notation designed specifically to help people describe and understand systems.
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