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

Identical Particles Revisited, Michael Fowler The Nature of Many-Electron Wavefunctions Quantum Mechanics and Quantum Computation at BerkeleyX Archived 2013-05-13...

The goal was to link the wavefunction that appears in Schrödinger's equation to a probability distribution in phase space. It is a generating function...

evolution is not a simple shift in wavefunction phase. The time-evolved states are, however, also coherent states but with phase-shifting parameter α instead:...

similar to quantum mechanics, based on a Hilbert space of complex, square-integrable wavefunctions. As its name suggests, the KvN theory is related to...

which have infinite norm, i.e. non-normalizable wavefunctions. Examples include states whose wavefunctions are Dirac delta functions or infinite plane waves...

gauge-invariant local manifestation of the geometric properties of the wavefunctions in the parameter space, and has proven to be an essential physical ingredient for...

they are governed by wavefunctions that give the probability of finding a particle at each position. As time passes, the wavefunctions tend to spread out...

regions of space can still be represented using a symmetrized/antisymmetrized wavefunction and that independent treatment of these wavefunctions gives the...

focal plane of objective lens Modify the wavefunction in reciprocal space by a phase factor, also known as the Phase Contrast Transfer Function, to account...

theory emerges from the Bohmian formalism when one considers conditional wavefunctions of subsystems. Pilot-wave theory is explicitly nonlocal, which is in...

wavefunctions that are covariants under the action of the group formed by multidimensional Linear Canonical Transformations. The quantum phase space (QPS)...

density. A more concise and experimentally relevant condition involves the phase-space density D = n λ T 3 {\displaystyle {\mathcal {D}}=n\lambda _{T}^{3}}...

forcing the pseudo-wavefunctions to coincide with the true valence wavefunctions beyond a certain distance rl. The pseudo-wavefunctions are also forced to...

the spatial variation of the phase of a wavefunction is said to characterize the probability flux of the wavefunction. Although the ∇ S m {\textstyle...

cancel if they have the same amplitude and their phases are spaced equally in angle. Using phasors, each wave can be represented as A e i φ n {\displaystyle...

combinations of atomic orbitals, or the sums and differences of the atomic wavefunctions, provide approximate solutions to the Hartree–Fock equations which correspond...

"smeared out" in space. For one-electron systems, the electron density at any point is proportional to the square magnitude of the wavefunction. In molecules...

decoherence does not reduce it to a single eigenstate. The concept of wavefunction collapse was introduced by Werner Heisenberg in his 1927 paper on the...

uncertainty relation: there is no uniquely defined phase operator in quantum mechanics. To find the wavefunction of the coherent state, the minimal uncertainty...

quantum state that can be described with a single, uniform wavefunction. In the gas phase, the Bose–Einstein condensate remained an unverified theoretical...

incoming wavefunctions or not, and how to merge the incoming wavefunctions can be controlled by experimenters. There are none of the phase differences...

normalization condition for the wave function states that if a wavefunction belongs to the quantum state space ψ ∈ L 2 ( R 3 ) , {\displaystyle \psi \in L^{2}(\mathbb...

principle; applied to many non-localized wavefunctions spread throughout the curved space to form a localized wavefunction: Ψ = ∑ n c n ψ n , {\displaystyle...

response to electric and magnetic fields, long decay periods and electron wavefunctions that approximate, under some conditions, classical orbits of electrons...

different wavenumbers, with phases and amplitudes such that they interfere constructively only over a small region of space, and destructively elsewhere...

Quantum states are either pure or mixed; pure states are also known as wavefunctions. Assigning a pure state to a quantum system implies certainty about...

accessible phase space. Thus, it would be natural to expect that the eigenstates of the quantum counterpart would fill the quantum phase space in the uniform...

The universe is all of space and time and their contents. It comprises all of existence, any fundamental interaction, physical process and physical constant...

waves, the phase velocity and the group velocity. Phase velocity is the rate at which the phase of the wave propagates in space: any given phase of the wave...