The phase-space formulation is a formulation of quantum mechanics that places the position and momentum variables on equal footing in phase space. The...

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...

the quantum phase space formulation and Hilbert space operators in the Schrödinger picture. Often the mapping from functions on phase space to operators...

functions on phase space, but as eigenvalues; more precisely as spectral values of linear operators in Hilbert space. These formulations of quantum mechanics...

time-dependent. In the phase-space formulation of quantum mechanics, substituting the Moyal brackets for Poisson brackets in the phase-space analog of the von...

referred to as a "microscopic state" Phase space formulation, a formulation of quantum mechanics in phase space Phase (waves), the position of a point in...

Phase-space representation of quantum state vectors is a formulation of quantum mechanics elaborating the phase-space formulation with a Hilbert space...

quantum mechanics to represent the phase space distribution of a quantum state such as light in the phase space formulation. It is used in the field of quantum...

a suggested way of writing down the phase space distribution of a quantum system in the phase space formulation of quantum mechanics. The P representation...

the phase space formulation of quantum mechanics, the symplectic phase space of classical mechanics is deformed into a non-commutative phase space generated...

satisfied by operator commutators on a Hilbert space and equivalently in the phase space formulation of quantum mechanics by the Moyal bracket. Let +...

Fermion Phase-space formulation Schrödinger equation Wave function collapse Wave packet The functions are here assumed to be elements of L2, the space of square...

system, where bounded classical trajectories are confined onto tori in phase space, tunnelling can be understood as the quantum transport between semi-classical...

symplectic space such that the leading term in the Taylor expansion over ħ of the commutator [A, B] expressed in the phase space formulation is iħ{A, B}...

mechanics and quantum mechanics Macroscopic quantum phenomena Phase-space formulation Regularization (physics) Two-state quantum system A momentum eigenstate...

Interaction picture Schrödinger picture Heisenberg–Langevin equations Phase space formulation "Heisenberg representation". Encyclopedia of Mathematics. Retrieved...

this phase-space formulation. There results a complete phase space formulation of quantum mechanics, completely equivalent to the Hilbert-space operator...

who pioneered the largely operator-free formulation of quantum mechanics in phase space known as phase-space quantization. Groenewold was born on 29 June...

useful and important, as it underlies the alternate equivalent phase space formulation of conventional quantum mechanics. In mathematical physics, geometric...

arise naturally in the study of quantum mechanics when treated in phase space formulation, commonly used in quantum optics, time-frequency analysis, and...

quantum expectation values, and hence quantum mechanics, in phase space (see Phase-space formulation). In most of his correspondence with Moyal in the mid-1940s...

location in the complex plane (phase space) is centered at the position and momentum of a classical oscillator of the phase θ and amplitude |α| given by...

and thereby describe quantum mechanical diffusion in phase space (See Phase space formulation and Wigner–Weyl transform). This more algebraic approach...

two into a common mathematical framework in various ways. In the phase space formulation of quantum mechanics, which is statistical in nature, logical connections...

This formulation has proven crucial to the subsequent development of theoretical physics, because manifest Lorentz covariance (time and space components...

representation change, however, Weyl's map underlies the alternate phase-space formulation of conventional quantum mechanics. Half-form Lagrangian foliation...

Koopman observed that the phase space of the classical system can be converted into a Hilbert space. According to this formulation, functions representing...

Matter wave Phase space formulation Uncertainty principle Ward's probability amplitude Wave packet The spanning set of a Hilbert space does not suffice for...

equation Interaction picture Heisenberg picture Phase space formulation POVM Mathematical formulation of quantum mechanics Schrödinger functional At t...

Quantum characteristics are phase-space trajectories that arise in the phase space formulation of quantum mechanics through the Wigner transform of Heisenberg...