Related papers: Refining spectroscopic calculations for trivalent …
Phase estimation is a quantum algorithm for measuring the eigenvalues of a Hamiltonian. We propose and rigorously analyse a randomized phase estimation algorithm with two distinctive features. First, our algorithm has complexity independent…
This paper discusses some features of the spectral line profile theory used in the treatment of measured atomic transitions. It is shown that going beyond the established linear approximation for the spectral line contour in the case of its…
A closed form expression for the three-electron Hylleraas integral involving the inverse quadratic power of one inter-particle coordinate is obtained, and recursion relations are derived for positive powers of other coordinates. This result…
A method for calculating the self energy part of the Lamb shift is revisited. When the electron propagator in an external field is represented as an expansion in partial waves, the original method converges relatively slowly, requiring the…
By the method of discrete transformation equations of 3-th wave hierarchy are constructed. We present in explicit form two Poisson structures, which allow to construct Hamiltonian operator consequent application of which leads to all…
We consider the solution of PT symmetry Hamiltonians using the technique of tridiagonal representation approach. This methodology provides more accurate results and proper depiction of the Hamiltonian energy level and wavefunctions. It is…
We present a method to compute the Fermi function of the Hamiltonian for a system of independent fermions, based on an exact decomposition of the grand-canonical potential. This scheme does not rely on the localization of the orbitals and…
A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a…
Rare earth ions in crystals exhibit narrow spectral features and hyperfine-split ground states with exceptionally long coherence times. These features make them ideal platforms for quantum information processing in the solid state.…
We introduce the concept of Hamiltonian potential variables to map Hamiltonian operators into symplectic operators in a dual space. This generalises the classical trick of switching to a potential variable to obtain a Lagrangian density for…
Lanthanide elements play important roles as an opacity source in the ejected material from neutron star mergers. Accurate and complete atomic data are necessary to evaluate the opacities and to analyze the observed data. In this paper, we…
The $4f-5d$ transition rates for rare-earth ions in crystals can be calculated with an effective transition operator acting between model $4f^N$ and $4f^{N-1}5d$ states calculated with effective Hamiltonian, such as semi-empirical crystal…
The variational procedure to construct compact and accurate wave functions for three-electron atoms and ions is developed. The procedure is based on the use of six-dimensional gaussoids written in the relative four-body coordinates $r_{12},…
Accurate models of alkali and halide ions in aqueous solution are necessary for computer simulations of a broad variety of systems. Previous efforts to develop ion force fields have generally focused on reproducing experimental measurements…
An exact invariant is derived for $n$-degree-of-freedom Hamiltonian systems with general time-dependent potentials. The invariant is worked out in two equivalent ways. In the first approach, we define a special {\it Ansatz\/} for the…
Low-temperature electron paramagnetic resonance measurements are performed on single crystals of LiY_{1-x}Gd_xF_4 with weak x=0.005 and moderate x=0.05 concentration of Gd ions. Modeling of the experimental spectra allows us to precisely…
Symmetry adaptation techniques are applied to the determination of the intensity of two-photon absorption transitions, between Stark levels of configurations with opposite parities, for transition ions in finite symmetry environments. The…
A general scheme for tridiagonalising differential, difference or q-difference operators using orthogonal polynomials is described. From the tridiagonal form the spectral decomposition can be described in terms of the orthogonality measure…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
Localized basis sets in the projector augmented wave formalism allow for computationally efficient calculations within density functional theory (DFT). However, achieving high numerical accuracy requires an extensive basis set, which also…