相关论文: How Are Quantum Eigenfunctions of Hydrogen Atom Re…
A novel approach is suggested for the statistical description of quantum systems of interacting particles. The key point of this approach is that a typical eigenstate in the energy representation (shape of eigenstates, SE) has a well…
Based on recent results on quasi-exactly solvable Schrodinger equations, we review a new phenomenological potential class lately reported. In the present paper we consider the quantum differential equations resulting from position dependent…
The orientation in space of a Cartesian coordinate system can be indicated by the two vectorial constants of motion of a classical Keplerian orbit: the angular momentum and the Laplace-Runge-Lenz vector. In quantum mechanics, the states of…
The classical trajectories of a particle governed by the PT-symmetric Hamiltonian $H=p^2+x^2(ix)^\epsilon$ ($\epsilon\geq0$) have been studied in depth. It is known that almost all trajectories that begin at a classical turning point…
Closed orbit theory is generalized to the semiclassical calculation of cross-correlated recurrence functions for atoms in external fields. The cross-correlation functions are inverted by a high resolution spectral analyzer to obtain the…
Semiclassical calculations using the Herman-Kluk initial value treatment are performed to determine energy eigenvalues of bound and resonance states of the collinear helium atom. Both the $eZe$ configuration (where the classical motion is…
We discuss the localization of wavefunctions along planes containing the shortest periodic orbits in a three-dimensional billiard system with axial symmetry. This model mimicks the self-consistent mean field of a heavy nucleus at…
We consider the quantum evolution $e^{-i\frac{t}{\hbar}H_{\beta}} \psi_{\xi}^{\hbar}$ of a Gaussian coherent state $\psi_{\xi}^{\hbar}\in L^{2}(\mathbb{R})$ localized close to the classical state $\xi \equiv (q,p) \in \mathbb{R}^{2}$, where…
A classical model of the hydrogen atom in a static electric field is studied, basing upon the work [ Hooker A. et al, {\it Phys. Rev. A}, 55 (1997) 4609 ]. In that work the electrons are supposed to move along Kepler orbits around the…
We provide arguments indicating that the semiclassical Einstein equations follow from quantum relative entropy and its proportionality to an area variation. Using modular theory, we establish that the relative entropy between the vacuum…
We consider the equatorial circular motion of a test particle of specific charge q/m << 1 in the Kerr-Newman geometry of a rotating charged black hole. We find the particle's conserved energy and conserved projection of the angular momentum…
We studied the orbit of an electron revolving around an infinitely massive nucleus of a large classical Hydrogen atom subject to an AC electric field oscillating perpendicular to the electron's circular orbit. Using perturbation theory in…
The position and momentum probability densities of a multidimensional quantum system are fully characterized by means of the radial expectation values $\langle r^\alpha \rangle$ and $\left\langle p^\alpha \right\rangle$, respectively. These…
The concept of dominant interaction hamiltonians is introduced and applied to classical planar electron-atom scattering. Each trajectory is governed in different time intervals by two variants of a separable approximate hamiltonian.…
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…
In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external…
Occupation numbers of natural orbitals capture the physics of strong electron correlations in momentum space. A Natural Orbital Density Functional Theory based on the antisymmetrized geminal product provides these occupation numbers and the…
The rise in linear entropy of a subsystem in the N-atom Jaynes-Cummings model is shown to be strongly influenced by the shape of the classical orbits of the underlying classical phase space: we find a one-to-one correspondence between…
Based on classical electrodynamics, it is argued that the Coulomb potential (which is strictly valid for two point charges at rest), commonly used in the study of energy levels of hydrogen atom is not the correct one, because the electron…
\emph{Probabilistic hysteresis} is a manifestation of irreversibility in a small, isolated classical system [Sci. Rep. 9, 14169]: after a slow cyclic sweep of a control parameter, the probability that a microcanonical ensemble returns to…