In quantum mechanics, Bra-ket notation is a standard notation for describing quantum states, composed of angle brackets and vertical bars.

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 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 >.

In the notation of the proof of Theorem 12, let us take a look at the special case in which the minimal polynomial for T is a product of first-degree polynomials, i.e., the case in which each Af is of the form Af.

An abugida ( from Ge ‘ ez አቡጊዳ ’ äbugida ), also called an alphasyllabary, is a segmental writing system in which consonant – vowel sequences are written as a unit: each unit is based on a consonant letter, and vowel notation is secondary.

The same notation is used with sets to denote cardinality ; the meaning depends on context.

In mathematical notation, this is:

In X-ray notation, the principal quantum number is given a letter associated with it.

The numeral system employed, known as algorism, is positional decimal notation.

As in so many programming languages, the operation ( V, x ) is often written V ← x ( or some similar notation ), and ( V ) is implied whenever a variable V is used in a context where a value is required.

( b ) illustrates the same process using spectroscopic notation,. The Auger effect () is a physical phenomenon in which the filling of an inner-shell vacancy of an atom is accompanied by the emission of an electron from the same atom.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

Either approach is adequate for most uses, provided that one attends to the necessary changes in language, notation, and the definitions of concepts like restrictions, composition, inverse relation, and so on.

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.

By the 13th century, with the widespread use of square notation, it is believed that most chant was sung with each note getting approximately an equal value, although Jerome of Moravia cites exceptions in which certain notes, such as the final notes of a chant, are lengthened.

For the length of a vector in Euclidean space ( which is an example of a norm, as explained below ), the notation | v | with single vertical lines is also widespread.

There were no textbooks on linear algebra as modern vector space and transformation theory, and the matrix notation of Arthur Cayley ( that unifies the subject ) had not yet come into widespread use.

This section draws upon the ideas, language and notation of canonical quantization of a quantum field theory.

Since virtually every calculation in quantum mechanics involves vectors and linear operators, it can involve, and often does involve, bra-ket notation.

In those disciplines we would write the product as ( the bra-ket notation of quantum mechanics ), respectively ( dot product as a case of the convention of forming the matrix product AB as the dot products of rows of A with columns of B ).

Suppose the state of a quantum system A, which we wish to copy, is ( see bra-ket notation ).

As is the tradition with any sort of quantum states, Dirac, or bra-ket notation, is used to represent them.

The following subsections are for those with a good working knowledge of the formal, mathematical description of quantum mechanics, including familiarity with the formalism and theoretical framework developed in the articles: bra-ket notation and mathematical formulation of quantum mechanics.

In the mathematical treatment of quantum mechanics, the theorem can be seen as a justification for the popular bra-ket notation.

* The left-hand portion,, of a bracket in bra-ket notation, a standard notation used in quantum mechanics

Grover's algorithm is a quantum algorithm for searching an unsorted database with N entries in O ( N < sup > 1 / 2 </ sup >) time and using O ( log N ) storage space ( see big O notation ).

A more rigorous derivation in Dirac notation shows how decoherence destroys interference effects and the " quantum nature " of systems.

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:

Such a bidirectional-arrow notation is frequently used for describing the probability current of quantum mechanics.

This notation is used extensively in quantum field theory where partial derivatives are usually indexed: so the lack of an index with the squared partial derivative signals the presence of the D ' Alembertian.

It is equivalent to the Schrödinger wave formulation of quantum mechanics, and is the basis of Dirac's bra-ket notation for the wave function.