The phase-space formulation of quantum mechanics places the position and momentum variables on equal footing in phase space. In contrast, the Schrödinger...

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...

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...

quantum expectation values, and hence quantum mechanics, in phase space (see Phase-space formulation). It has applications in statistical mechanics, quantum...

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

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...

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

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

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

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...

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

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

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

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...

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

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...

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

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

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}...

}e^{(2n+1)\left(x-{\tfrac {1}{2}}\sinh(2x)\right)}dx~.} In the phase space formulation of quantum mechanics, eigenstates of the quantum harmonic oscillator...

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

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

4\sigma _{B},} while for pure states the equality holds. In the phase space formulation of quantum mechanics, the Robertson–Schrödinger relation follows...

properties. In space, amorphous ice is the most common form as confirmed by observation. Thus, it is theorized to be the most common phase in the universe...

observables in the phase space formulation of quantum mechanics when these observables are described as functions on phase space. It relies on schemes...

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...

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

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