Search results
Results from the WOW.Com Content Network
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.
However, since s is an unphysical parameter, physical states must be left invariant by "s-evolution", and so the physical state space is the kernel of H − E (this requires the use of a rigged Hilbert space and a renormalization of the norm). This is related to the quantization of constrained systems and quantization of gauge theories. It is ...
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 .
If the size of the state space is finite, calculating the size of the state space is a combinatorial problem. [4] For example, in the Eight queens puzzle, the state space can be calculated by counting all possible ways to place 8 pieces on an 8x8 chessboard. This is the same as choosing 8 positions without replacement from a set of 64, or
The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space.The two key features of the phase-space formulation are that the quantum state is described by a quasiprobability distribution (instead of a wave function, state vector, or density matrix) and operator multiplication is replaced by a star product.
An observable is some real-valued function f on the state space. Examples of observables are position, momentum or energy of a particle. For classical systems, the value f(x), that is the value of f for some particular system state x, is obtained by a process of measurement of f.
The system's evolving state over time traces a path (a phase-space trajectory for the system) through the high-dimensional space. The phase-space trajectory represents the set of states compatible with starting from one particular initial condition , located in the full phase space that represents the set of states compatible with starting from ...
The adjoint state space is chosen to simplify the physical interpretation of equation constraints. [3] Adjoint state techniques allow the use of integration by parts, resulting in a form which explicitly contains the physically interesting quantity. An adjoint state equation is introduced, including a new unknown variable.