What does quantum state mean?

Definitions for quantum state
quan·tum state

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Wiktionary

  1. quantum statenoun

    any of the possible states of a quantum mechanical system

Wikipedia

  1. Quantum state

    In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement on a system. Knowledge of the quantum state together with the rules for the system's evolution in time exhausts all that can be predicted about the system's behavior. A mixture of quantum states is again a quantum state. Quantum states that cannot be written as a mixture of other states are called pure quantum states, while all other states are called mixed quantum states. A pure quantum state can be represented by a ray in a Hilbert space over the complex numbers, while mixed states are represented by density matrices, which are positive semidefinite operators that act on Hilbert spaces.Pure states are also known as state vectors or wave functions, the latter term applying particularly when they are represented as functions of position or momentum. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vectors are identified by the principal quantum number n, the angular momentum quantum number ℓ, the magnetic quantum number m, and the spin z-component sz. For another example, if the spin of an electron is measured in any direction, e.g. with a Stern–Gerlach experiment, there are two possible results: up or down. The Hilbert space for the electron's spin is therefore two-dimensional, constituting a qubit. A pure state here is represented by a two-dimensional complex vector ( α , β ) {\displaystyle (\alpha ,\beta )} , with a length of one; that is, with where | α | {\displaystyle |\alpha |} and | β | {\displaystyle |\beta |} are the absolute values of α {\displaystyle \alpha } and β {\displaystyle \beta } . A mixed state, in this case, has the structure of a 2 × 2 {\displaystyle 2\times 2} matrix that is Hermitian and positive semi-definite, and has trace 1.

Wikidata

  1. Quantum state

    In quantum physics, quantum state refers to the state of a quantum system. A quantum state is given as a vector in a Hilbert space, called the state vector. The state vector theoretically contains statistical information about the quantum system. For example, when dealing with the energy spectrum of the electron in a hydrogen atom, the relevant state vector is given by the principal quantum number . For a more complicated case, consider Bohm formulation of EPR experiment, where the state vector involves superposition of joint spin states for 2 different particles. In a more general usage, a quantum state can be either "pure" or "mixed." The above example is pure. Mathematically, a pure quantum state is represented by a state vector in a Hilbert space, which is a generalization of our more usual three dimensional space. A mixed quantum state corresponds to a probabilistic mixture of pure states; however, different distributions of pure states can generate equivalent mixed states. Quantum states, mixed as well as pure, are described by so-called density matrices, although these give probabilities, not densities. For example, if the spin of an electron is measured in any direction, e.g., with a Stern-Gerlach experiment, there are two possible results, up or down. The Hilbert space for the electron's spin is therefore two-dimensional. A pure state is a two-dimensional complex vector, with a length of one. That is,

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Numerology

  1. Chaldean Numerology

    The numerical value of quantum state in Chaldean Numerology is: 8

  2. Pythagorean Numerology

    The numerical value of quantum state in Pythagorean Numerology is: 1

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"quantum state." Definitions.net. STANDS4 LLC, 2024. Web. 28 Mar. 2024. <https://www.definitions.net/definition/quantum+state>.

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