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In 2004 Oliveira et al. developed a new wave-function formalism in phase space where the wave-function is associated to the Wigner quasiprobability distribution by means of the Moyal product. [6] An advantage might be that off-diagonal Wigner functions used in superpositions are treated in an intuitive way, ψ 1 ⋆ ψ 2 {\displaystyle \psi _{1 ...
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.
The phase velocity varies with frequency. The phase velocity is the rate at which the phase of the wave propagates in space. The group velocity is the rate at which the wave envelope, i.e. the changes in amplitude, propagates. The wave envelope is the profile of the wave amplitudes; all transverse displacements are bound by the envelope profile.
[6] Quantum characteristics must be distinguished from the trajectories of the De Broglie–Bohm theory, [11] the trajectories of the path-integral method in phase space for the amplitudes [12] and the Wigner function, [13] [14] and the Wigner trajectories. [5]
The phase space of a physical system is the set of all possible physical states of the system when described by a given parameterization. Each possible state corresponds uniquely to a point in the phase space. For mechanical systems, the phase space usually consists of all possible values of the position and momentum parameters.
Optical phase diagram of a coherent state's distribution across phase space. In quantum optics, an optical phase space is a phase space in which all quantum states of an optical system are described. Each point in the optical phase space corresponds to a unique state of an optical system.
Homogeneity of space is fundamental to quantum field theory (QFT) where the wave function of any object propagates along all available unobstructed paths. When integrated along all possible paths , with a phase factor proportional to the action , the interference of the wave-functions correctly predicts observable phenomena.
The configuration space is different for different versions of pilot-wave theory. For example, this may be the space of positions Q k {\displaystyle \mathbf {Q} _{k}} of N {\displaystyle N} particles, or, in case of field theory, the space of field configurations ϕ ( x ) {\displaystyle \phi (x)} .