Related papers: Hydrogen atom in phase space: The Wigner represent…
Starting from Feynman's Lagrangian description of quantum mechanics, we propose a method to construct explicitly the propagator for the Wigner distribution function of a single system. For general quadratic Lagrangians, only the classical…
We follow and modify the Feshbach-Villars formalism by separating the Klein-Gordon equation into two coupled time-dependent Schroedinger equations for particle and antiparticle wave function components with positive probability densities.…
A partial separation of the variables is practicable for the solution of Schroedinger's temporally independent equation in cartesian coordinates x,y,z, which yields moderately simple algebraic formulae for the amplitude functions involving…
We present exact energy spectrum and eigenfunctions of the one-dimensional hydrogen atom in the presence of the minimal length uncertainty. By requiring the self-adjointness property of the Hamiltonian, we completely determine the…
Wigner distributions play a significant role in formulating the phase space analogue of quantum mechanics. The Schrodinger wave-functional for solitons is needed to derive it for solitons. The Wigner distribution derived can further be used…
The Wigner function, which provides a phase-space description of quantum systems, has various applications in quantum mechanics, quantum kinetic theory, quantum optics, radiation transport and others. The concept of Wigner function has been…
The solution of Dirac's equation for the hydrogen atom according to relativistic wave mechanics yields for each state a vectorial amplitude function with four components, two large and two small. Each such component has its characteristic…
We introduce the Wigner functional representing a quantum field in terms of the field amplitudes and their conjugate momenta. The equation of motion for the functional of a scalar field point out the relevance of solutions of the classical…
The Wigner function's behavior of accelerated and non-accelerated Greenberger Horne Zeilinger (GHZ) state is discussed. For the non-accelerated GHZ state, the minimum/maximum peaks of the Wigner function depends on the distribution's…
We propose a methodology to design Wigner representations in phase spaces with nontrivial topology having evolution equations with desired mathematical properties. As an illustration, two representations of molecular rotations are developed…
The Wigner function shares several properties with classical distribution functions on phase space, but is not positive-definite. The integral of the Wigner function over a given region of phase space can therefore lie outside the interval…
We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…
We represent both the states and the evolution of a quantum computer in phase space using the discrete Wigner function. We study properties of the phase space representation of quantum algorithms: apart from analyzing important examples,…
This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions and star-products, following a technique developed earlier, {\it viz\/,} using the unitary…
Representations of the Poincar\'{e} symmetry are studied by using a Hilbert space with a phase space content. The states are described by wave functions ( quasi amplitudes of probability) associated with Wigner functions (quasi probability…
A quantum state can be written in phase space, but the resulting object is not generally the probability density of a positive stochastic process on ordinary phase space. We spell this out for Wigner dynamics. If a positive phase-space…
The Lorentz contraction of bound states in field theory is often appealed to in qualitative descriptions of high energy particle collisions. Surprisingly, the contraction has not been demonstrated explicitly even in simple cases such as the…
We consider a non-relativistic two-dimensional (2D) hydrogen-like atom in a weak, static, uniform magnetic field perpendicular to the atomic plane. Within the framework of the Rayleigh-Schr\"odinger perturbation theory, using the Sturmian…
We examine the visualization of quantum mechanics in phase space by means of the Wigner function and the Wigner function flow as a complementary approach to illustrating quantum mechanics in configuration space by wave functions. The Wigner…
Non-classical states are of practical interest in quantum computing and quantum metrology. These states can be detected through their Wigner function negativity in some regions. In this paper, we calculate the ground state of the…