Related papers: Quantum phase space with a basis of Wannier functi…

Mathematical method of quantum phase space is very useful in physical applications like quantum optics and non-relativistic quantum mechanics. However, attempts to generalize it for the relativistic case lead to some difficulties. One of…

We present a phase space description of the process of quantum teleportation for a system with an $N$ dimensional space of states. For this purpose we define a discrete Wigner function which is a minor variation of previously existing ones.…

In this paper, we study within the structure of Symplectic Quantum Mechanics a bi-dimensional non-relativistic strong interaction system which represent the bound state of heavy quark-antiquark, where we consider a Cornell potential which…

The paper develop the alternative formulation of quantum mechanics known as the phase space quantum mechanics or deformation quantization. It is shown that the quantization naturally arises as an appropriate deformation of the classical…

The Weyl-Wigner representation of quantum mechanics allows one to map the density operator in a function in phase space - the Wigner function - which acts like a probability distribution. In the context of statistical mechanics, this…

For classical canonical transformations, one can, using the Wigner transformation, pass from their representation in Hilbert space to a kernel in phase space. In this paper it will be discussed how the time-dependence of the uncertainties…

On the basis of the phase states, we present the correct integral expressions of the two number-phase Wigner functions discovered so far. These correct forms are derived from those defined in the extended Fock space with negative number…

Given its well known spectral decomposition profile, the $1$-dim harmonic oscillator potential modified by an inverse square ($1$-dim angular momentum-like) contribution works as an efficient platform for probing classical and quantum…

The Fermi g_F(x,p) function provides a phase space description of quantum mechanics conceptually different from that based on the the Wigner function W(x,p). In this paper, we show that for a peaked wave packet the g_F(x,p)=0 curve…

The nodal structure of bound-state wave functions for one-dimensional quantum systems with quartic energy-momentum dispersion and polynomial potentials is analysed by using the semiclassical approximation and variational approach. For…

We develop the Wigner phase space representation of a kicked particle for an arbitrary but periodic kicking potential. We use this formalism to illustrate quantum resonances and anti--resonances.

Using the phase-space formulation of quantum mechanics, we derive a four-component Wigner equation for a system composed of spin-1/2 fermions (typically, electrons) including the Zeeman effect and the spin-orbit coupling. This Wigner…

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's Theorem. In the phase-space…

A set of exactly computable orthonormal basis functions that are useful in computations involving constituent quarks is presented. These basis functions are distinguished by the property that they fall off algebraically in momentum space…

We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient…

The Wigner eigenfunctions of a free quantum particle propagating on a plane are derived. Two possibilities are analysed. Firstly, the particle of given energy and angular momentum is discussed. In that case, a special choice of coordinates…

We review the problem of state reconstruction in classical and in quantum physics, which is rarely considered at the textbook level. We review a method for retrieving a classical state in phase space, similar to that used in medical imaging…

Classical surfaces in phase space correspond to quantum states in Hilbert space. Subsystems specify factor spaces of the Hilbert space. An entangled state corresponds semiclassically to a surface that cannot be decomposed into a product of…

A discussion of discrete Wigner functions in phase space related to mutually unbiased bases is presented. This approach requires mathematical assumptions which limits it to systems with density matrices defined on complex Hilbert spaces of…

We address the question of which phase space functionals might represent a quantum state. We derive necessary and sufficient conditions for both pure and mixed phase space quantum states. From the pure state quantum condition we obtain a…