Related papers: Elliptical orbits in the phase-space quantization

The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…

The circular orbits and elliptical orbits of moving objects in a gravitational field are essential information in astronomy. There have been many methods developed in the literature and textbooks to describe these orbits. In this report, I…

Nonintegrable dynamical systems have complex structures in their phase space. Motion of a test charged particle in a dipole magnetic field can be reduced to a 2 degree-of-freedom (2 d.o.f.) nonintegrable Hamiltonian system. We carried out a…

Recent results on the semiclassical dynamics of an electron in a solid are explained using techniques developed for ``exotic'' Galilean dynamics. The system is indeed Hamiltonian and Liouville's theorem holds for the symplectic volume form.…

We give a formulation of quantum ergodicity for Pauli Hamiltonians with arbitrary spin in terms of a Wigner-Weyl calculus. The corresponding classical phase space is the direct product of the phase space of the translational degrees of…

We first discuss the use of dimensional arguments (and of the quadrupolar emission hypothesis) in the derivation of the gravitational power radiated on a circular orbit. Then, we show how to simply obtain the instantaneous power radiated on…

The energy spectrum and corresponding wave functions of a flat quantum dot with elliptic symmetry are obtained exactly. A detailed study is made of the effect of ellipticity on the energy levels and the corresponding wave functions. The…

A phase space mathematical formulation of quantum mechanical processes accompanied by and ontological interpretation is presented in an axiomatic form. The problem of quantum measurement, including that of quantum state filtering, is…

We review Bohr's atomic model and its extension by Sommerfeld from a mathematical perspective of wave mechanics. The derivation of quantization rules and energy levels is revisited using semiclassical methods. Sommerfeld-type integrals are…

We treat the classical dynamics of the hydrogen atom in perpendicular electric and magnetic fields as a celestial mechanics problem. By expressing the Hamiltonian in appropriate action-angle variables, we separate the different time scales…

Circuit quantization is an extraordinarily successful theory that describes the behavior of quantum circuits with high precision. The most widely used approach of circuit quantization relies on introducing a classical Lagrangian whose…

The energy levels of hydrogen-like atom on a noncommutative phase space were studied in the framework of relativistic quantum mechanics. The leading order corrections to energy levels 2S_{1/2}, 2P_{1/2} and 2P_{3/2} were obtained by using…

Unlike the previous theoretical results based on standard quantum mechanics that has established the nearly elliptical shapes for the centre-of-mass motion using numerical simulations, we show analytically that the Bohmian trajectories in…

We present an analytic method, based on the Bohmian equations for quantum mechanics, for approaching the phase-retrieval problem in the following formulation: By knowing the probability density $\left\vert…

We introduce phase operators associated with the algebra su(3), which is the appropriate tool to describe three-level systems. The rather unusual properties of this phase are caused by the small dimension of the system and are explored in…

We study the phase space of a particle moving in the gravitational field of a rotating black hole described by the Kerr metric from a geometrical perspective. In particular, we show the construction of a multidimensional generalization of…

Within the framework of loop quantum cosmology, there exists a semi-classical regime where spacetime may be approximated in terms of a continuous manifold, but where the standard Friedmann equations of classical Einstein gravity receive…

In this paper it is shown that the quantum state of a multiverse made up of classically disconnected regions of the space-time, whose dynamical evolution is dominated by a homogeneous and isotropic fluid, is given by a squeezed state. These…

We introduce a quantum phase space representation for the orientation state of extended quantum objects, using the Euler angles and their conjugate momenta as phase space coordinates. It exhibits the same properties as the standard Wigner…

The $n$ integrals in involution for the motion on the $n$-dimensional ellipsoid under the influence of a harmonic force are explicitly found. The classical separation of variables is given by the inverse momentum map. In the quantum case…