Phase Space

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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. Fixed points are easily found to lie at y 0 and x kπ k integer. For mechanical systems the phase space usually consists of all possible values of position and momentum variables.

See phasespace in action. In classical mechanics the phase space is the space of all possible states of a physical system. D2x dt2 sin x 0.

The corresponding phase space is a cylinder t1 rperiodic in the x direction. For a system of first order ordinary differential equations or more generally pfaffian forms the dimensional space consisting of the possible values of is known as its phase space. The term phase space refers to coordinates of a dynamic system in which the state of the system is recorded over time.

If the phase space is known as a phase plane. In quantum mechanics the phase space is a complex hilbert space though for a quantum system with a classical analogue the phase space often means the phase space of this analogue. Dx dt y dy dt sin x.

In the theory of stochastic processes the phase space is the measurable space often with an additional topological differentiable or vector structure in which the process takes values. We live instead in a place called phase space. To envision the concept imagine a swarm of bees that are localized to the yard in which the bee hive is located.

In contrast the schrödinger picture uses the position or momentum representations see also position and momentum space. In dynamical system theory a phase space is a space in which all possible states of a system are represented with each possible state corresponding to one unique point in the phase space. They say we need to forget about the home einstein invented for us.