- #1
kweierstrass
- 4
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What is meant when writing a "one-ket" like this |1> ?
http://en.wikipedia.org/wiki/Bra-ket_notation#Most_common_use:_Quantum_mechanics"
In quantum mechanics, the state of a physical system is identified with a ray in a complex separable Hilbert space, [tex]\mathcal{H}[/tex], or, equivalently, by a point in the projective Hilbert space of the system. Each vector in the ray is called a "ket" and written as [tex]|\psi\rangle[/tex], which would be read as "ket psi". (The [tex]\psi\![/tex] can be replaced by any symbols, letters, numbers, or even words—whatever serves as a convenient label for the ket.) The ket can be viewed as a column vector and (given a basis for the Hilbert space) written out in components,
[tex]|\psi\rangle = [ c_0 \; c_1 \; c_2 \; \dots ] ^T, [/tex]
when the considered Hilbert space is finite-dimensional. In infinite-dimensional spaces there are infinitely many components and the ket may be written in complex function notation, by prepending it with a bra (see below). For example,
[tex]\langle x|\psi\rangle = \psi(x)\ = c e^{- ikx}.[/tex]
A notational question is a type of question that is used in mathematical and scientific fields to express a concept or idea in a concise and standardized way. It typically involves using symbols, notation, or language that is commonly understood by those in the field.
The symbol |1> is commonly used in notational questions to represent a state vector, particularly in the field of quantum mechanics. It can also be used to represent a basis vector or a unit vector in linear algebra.
In notational questions, |1> and |0> are often used to represent different states or conditions. For example, in quantum mechanics, |1> may represent an excited state while |0> represents a ground state. In linear algebra, |1> can represent a vector in one direction while |0> represents a vector in the opposite direction.
The use of |1> in notational questions is significant because it allows for a more concise and universal representation of concepts and ideas. This allows for easier communication and understanding within the scientific community. Additionally, the use of this symbol in quantum mechanics has led to important discoveries and advancements in the field.
Notational questions are used extensively in scientific research to express and analyze complex concepts and data. They allow for a standardized and precise way of communicating ideas and findings, which is crucial in the scientific community. Notational questions are also used to formulate hypotheses, design experiments, and interpret results in various fields of science.