Related papers: Refining spectroscopic calculations for trivalent …
Local density approximation (LDA) to the density functional theory (DFT) has continuous derivative of total energy as a number of electrons function and continuous exchange-correlation potential, while in exact DFT both should be…
We calculate the exceptional points of the eigenvalues of several parameter-dependent Hamiltonian operators of mathematical and physical interest. We show that the calculation is greatly facilitated by the application of the discriminant to…
It is well know that many full atomic multiplet codes are available for experimentalists to check x-ray absorption or emission spectra against known valence materials to identify effect valence configuration of transition metal ions as well…
Spectral decomposition of matrices is a recurring and important task in applied mathematics, physics and engineering. Many application problems require the consideration of matrices of size three with spectral decomposition over the real…
A recently proposed approach for performing electronic-structure calculations on crystalline insulators in terms of localized orthogonal orbitals is applied to the oxides of lithium and sodium, Li2O and Na2O. Cohesive energies, lattice…
Lanthanides are often used as surrogates to study the properties of actinide compounds. Their behaviour is considered to be quite similar as they both possess f valence electrons and are close in size and chemical properties. This study…
We perform accurate calculations of the dependence of transition frequencies in two valence electron atoms and ions on a variation of the fine structure constant, alpha. The relativistic Hartree-Fock method is used with many-body…
The linear canonical wavelet transform has been shown to be a valuable and powerful time-frequency analyzing tool for optics and signal processing. In this article, we propose a novel transform called quaternion linear canonical wavelet…
The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators. In terms of usual differential equations the main content can be presented…
The information of quantum pathways can be extracted in the framework of the Hamiltonian-encoding and Observable-decoding method. For closed quantum systems, only off-diagonal elements of the Hamiltonian in the Hilbert space is required to…
In the context of loop quantum cosmology, we parametrise the lattice refinement by a parameter, $A$, and the matter Hamiltonian by a parameter, $\delta$. We then solve the Hamiltonian constraint for both a self-adjoint, and a…
We use the Foldy--Wouthuysen (unitary) transformation to give an alternative characterization of the eigenvalues and eigenfunctions for the Brown-Ravenhall operator (the projected Dirac operator) in the case of a one-electron atom. In…
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algebraic and differential-geometric properties. We apply our…
Central quantities in spectroscopy and magnetism of transition ions in crystals are crystal field parameters (CFPs). Nature self-imposed limits on orthorhombic and lower symmetry CFPs, and existence of intrinsically incomparable CFP sets…
A number of many-body problems can be formulated using Hamiltonians that are quadratic in the creation and annihilation operators. Here, we show how such quadratic Hamiltonians can be efficiently estimated indirectly, employing very few…
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…
A successful and commonly used ab initio method for the calculation of crystal field levels and magnetic anisotropy of lanthanide complexes consists of spin-adapted state-averaged CASSCF calculations followed by state interaction with…
The energy levels of the first few low-lying states of helium and lithium atoms in intense magnetic fields up to $\approx 10^8-10^9$~T are calculated in this study. A pseudospectral method is employed for the computational procedure. The…
Harrison's tight-binding theory provides an excellent qualitative description of the electronic structure of the elements across the periodic table. However, the resulting band structures are in significant disagreement with those found by…
A variational calculation of the energy levels of a class of PT-invariant quantum mechanical models described by the non-Hermitian Hamiltonian H= p^2 - (ix)^N with N positive and x complex is presented. Excellent agreement is obtained for…