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 was designed to facilitate the formal manipulation of linear-algebraic 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 >.

Postfix notation makes the language easier to parse and extend ; Forth's flexibility makes a static BNF grammar inappropriate, and it does not have a monolithic compiler.

MIDI sequencing makes it possible for a user with no notation skills to build complex arrangements.

The language syntax uses reverse Polish notation, which makes the order of operations unambiguous, but reading a program requires some practice, because one has to keep the layout of the stack in mind.

* Pierre de Fermat makes a notation, in a document margin, claiming to have proof of what would become known as Fermat's last theorem.

Because it is based on a tabular notation, it makes the underlying triples encoded in the documents more easily recognizable compared to the XML serialization.

Formal notation makes it possible to automate the task of validating whether a specific instance of data representation abides by the specifications.

Strictly speaking, del is not a specific operator, but rather a convenient mathematical notation for those three operators, that makes many equations easier to write and remember.

They replace the master hit with the notions of good attack ( the attacker makes a throw equal to or less than the good attack score, as shown on a table in relation to her attack score ) and good parry ( five points less than the parry score with the d20 in dice notation ).

This change in notation ( choosing the tie rather than the longer note value ) does not affect performance, but it makes the music easier to read.

One is called the plus-cylinder notation ( or " plus cyl ") and the other the minus-cylinder notation ( or " minus cyl "), based upon whether the axis chosen makes the cylindrical correction a positive or negative number.

This notation makes an easy way to express the sum of all the coefficients of Layer n:

Indexing with numbered notation makes it possible to search a piece of music by melody rather than by title.

There is also a brief scene ( taken from a notation in the short story and included to avoid depicting Mowgli's nudity ) in which he steals some cloth and makes himself a loin cloth after seeing humans wearing clothes.

This article makes use of the first notation.

This program makes use of Sibelius notation software, which allows people to compose music electronically.

This notation makes the exotic nature of the random function of time in the physics formulation more explicit.

The letter " d " is used, as is " t " to denote both " High G " and " D " grace notes, but an examination of the notation word, makes a mistake unlikely, thus " dieliu " means " F " with " high G " grace note, and then " high A " and " G ".

Although there are many ways to represent control characters, this correspondence between notation and typing makes the caret notation suitable for many applications.

The software makes use of multiple instrument tracks which follow standard staff notation, but also shows the notes on tablature notation.

Together with a sequent notation for clauses, a tree representation also makes it clear to see how the resolution rule is related to a special case of the cut-rule, restricted to atomic cut-formulas.

An example of such a finite field is the ring Z / pZ, which is essentially the set of integers from 0 to p − 1 with integer addition and multiplication modulo p. It is also sometimes denoted Z < sub > p </ sub >, but within some areas of mathematics, particularly number theory, this may cause confusion because the same notation Z < sub > p </ sub > is used for the ring of p-adic integers.

He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.

Sometimes ( particularly for operas in the public domain ) this format is supplemented with melodic excerpts of musical notation for important numbers.

Wolf's writings on the history of musical notation are considered to be particularly notable by musicologists.

Note however, that it is not uncommon to express aqueous concentrations — particularly in drinking-water reports intended for the general public — using parts-per notation ( 2. 1 ppm, 0. 8 ppb, etc.

In physics, particularly in quantum mechanics, the spectral theorem is expressed in a way which combines the spectral theorem as stated above and the Borel functional calculus using Dirac notation as follows:

The following is only an introduction to the concept: index notation is used in more detail in mathematics ( particularly in the representation and manipulation of tensor operations ).

Such compromise editions are particularly useful for early music, where the interpretation of the musical notation of long ago often poses difficulties.

The early notation of plainchant, particularly Gregorian chant, used a series of shapes called neumes, which served as reminders of music that was taught by rote rather than as an exact record of which notes were to be sung.

The construction and format of the notation make it particularly suited to computer generation of symmetry information.

* Q100, a conventional notation for the 100-year flood, particularly in hydrology

* Tablature, a form of musical notation used particularly for guitars and other fretted instruments

While his authorship and the very existence of this treatise have recently come into question, a handful of his musical works do survive and show the innovations in musical notation, particularly mensural and rhythmic, with which he was credited within a century of their inception.

The term engraving is now used to refer to any high-quality method of drawing music notation, particularly on a computer (" computer engraving " or " computer setting ") or by hand (" hand engraving ").

Some Sacred Harp leaders ( particularly James and his colleagues ) responded by rejecting both the gospel style and the seven-shape notation.

The notation is sometimes used in the context of meantone temperament, and does not always assume equal temperament nor the standard concert A of 440 Hz ; this is particularly the case in connection with earlier music.

, also known as kuchi showa or kuchi shoka, is an educational musical notation for traditional Japanese drums, particularly the taiko and the tsuzumi.

* The notation for groups of type D < sub > n </ sub > (" orthogonal " groups ) is particularly confusing.

Caret notation is used in many programs, particularly Unix terminal drivers and text file viewers such as more and less.

After the fall of Kievan Rus ' to the mongols, the Znamenny Chant and stolp notation continued to develop to the North ( particularly in Novgorod ), where it flourished and was adopted throughout the Grand Duchy of Moscow.

In the 19th century Edinovertsy, particularly outside Russia, have tried to move to the modern neume form of notation that tries to capture exact relations between pitches ; and they currently use a standard linear notation.