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In functional analysis, a state of an operator system is a positive linear functional of norm 1. States in functional analysis generalize the notion of density matrices in quantum mechanics, which represent quantum states , both mixed states and pure states .
A quantum state in the Fock space is called a Fock state if it is an element of the occupancy number basis. A Fock state satisfies an important criterion: for each i, the state is an eigenstate of the particle number operator ^ corresponding to the i-th elementary state k i. The corresponding eigenvalue gives the number of particles in the state.
The coefficient that corresponds to a particular state in the linear combination is a complex number, thus allowing interference effects between states. The coefficients are time dependent. How a quantum state changes in time is governed by the time evolution operator .
The term phase is sometimes used as a synonym for state of matter, but it is possible for a single compound to form different phases that are in the same state of matter. For example, ice is the solid state of water, but there are multiple phases of ice with different crystal structures , which are formed at different pressures and temperatures.
Energy levels for an electron in an atom: ground state and excited states. After absorbing energy, an electron may jump from the ground state to a higher-energy excited state. The ground state of a quantum-mechanical system is its stationary state of lowest energy; the energy of the ground state is known as the zero-point energy of the system.
The state space or phase space is the geometric space in which the axes are the state variables. The system state can be represented as a vector, the state vector. If the dynamical system is linear, time-invariant, and finite-dimensional, then the differential and algebraic equations may be written in matrix form.
The standard state of a material (pure substance, mixture or solution) is a reference point used to calculate its properties under different conditions.A degree sign (°) or a superscript Plimsoll symbol (⦵) is used to designate a thermodynamic quantity in the standard state, such as change in enthalpy (ΔH°), change in entropy (ΔS°), or change in Gibbs free energy (ΔG°).
In information technology and computer science, a system is described as stateful if it is designed to remember preceding events or user interactions; [1] the remembered information is called the state of the system. The set of states a system can occupy is known as its state space. In a discrete system, the state space is countable and often ...