Related papers: Semiclassical initial value calculations of collin…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
We compute quasinormal mode frequencies for static limits of physical black holes - semi-classical black hole solutions to Einstein-Hilbert gravity characterized by the finite formation time of an apparent horizon and its weak regularity.…
The Dirac-Coulomb equation for helium-like ions is solved using the iterative self-consistent field method, with Slater-type spinor orbitals as the basis. These orbitals inherently satisfy the kinetic-balance condition due to their coupling…
Energy levels of the $1sns$ and $1snp$ states of ions along the helium isoelectronic sequence from carbon to uranium are calculated, with $n=3$-$7$. The computation is performed within the relativistic configuration-interaction method,…
Semiclassical spectra weighted with products of diagonal matrix elements of operators A_{alpha}, i.e., g_{alpha alpha'}(E) = sum_n <n|A_{alpha}|n><n|A_{alpha'}|n>/(E-E_n) are obtained by harmonic inversion of a cross-correlation signal…
We consider the semiclassical quantization of sine-Gordon solitons on the circle with periodic and anti-periodic boundary conditions. The 1-loop quantum corrections to the mass of the solitons are determined using zeta function…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
A calculation of the classical analogue for the quantum wave function and local denity of states, in energy representation, is presented for simple Hamiltonian systems. Sucha analogous were proposed by M. V. Berry and A. voros considering…
Using the algebro-geometric approach, we study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain. We outline how classical nonlinear spin waves governed by the anisotropic Landau-Lifshitz…
We consider the problem of defining a microcanonical thermofield double state at fixed energy and angular momentum from the gravitational path integral. A semiclassical approximation to this state is obtained by imposing a mixed boundary…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
We calculate the energies of ground and three low lying excited states of confined helium atom centered in an impenetrable spherical box. We perform the calculation by employing variational method with two-parameter variational forms for…
We present a novel analytical method for calculating the spectral function and the density of states in speckle potentials, valid in the semiclassical regime. Our approach relies on stationary phase approximations, allowing us to describe…
In this communication, we present an efficient method for computation of energy and wave function of weakly bound nuclei by the application of supersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC) technique. As a case…
Semiclassical oscillation of the electron through the nucleus of the H atom yields both the exact energy and the correct orbital angular momentum for l=0 quantum states. Similarly, electron oscillation through the nuclei of H2+ accounts for…
In this work we semiclassically analyzed the high lying eigenstates of a mixed type Hamiltonian system. For the regular states we employ the Einstein-Brillouin-Keller quantization, while for the chaotic states, following the principle of…
In this work we present the results of a numerical and semiclassical analysis of high lying states in a Hamiltonian system, whose classical mechanics is of a generic, mixed type, where the energy surface is split into regions of regular and…
The numerical treatment of quantum mechanics in the semi-classical regime is known to be computationally demanding, due to the highly oscillatory behaviour of the wave function and its large spatial extension. A recently proposed…
We show that a highly-excited energy eigenfunction $\psi_{nlm}(\vec{r})$ of hydrogen atom can be approximated as an equal-weight superposition of classical elliptic orbits with energy $E_n$ and angular momentum $L=\sqrt{l(l+1)}\hbar$, and…
We study quantum mechanically the self-similar black hole formation by collapsing scalar field and find the wave functions that give the correct semiclassical limit. In contrast to classical theory, the wave functions for the black hole…