Related papers: Compact variational wave functions for bound state…
A simple, seven-parameter trial function is proposed for a description of the ground state of the Lithium atom. It includes both spin functions. Inter-electronic distances appear in exponential form as well as in a pre-exponential factor,…
Several ultra-compact accurate wave functions in the form of generalized Hylleraas-Kinoshita functions and Guevara-Harris-Turbiner functions, which describe the domain of applicability of the Quantum Mechanics of Coulomb Charges (QMCC), or,…
A rigorous characterization of the information content of any highest-spin three-fermion wave function is presented. It is based upon a formal decomposition of the wave function into a finite set of fixed invariants, called shapes, whose…
A variational technique to describe the ground and scattering states below the break-up threshold for a three-nucleon system is developed. The method consists in expanding the wave function in terms of correlated Harmonic Hyperspherical…
Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…
A method to calculate the bound states of three-atoms without resorting to an explicit partial wave decomposition is presented. The differential form of the Faddeev equations in the total angular momentum representation is used for this…
A general procedure for the optimization of atomic density-fitting basis functions is designed with the balance between accuracy and numerical stability in mind. Given one-electron wavefunctions and energies, weights are assigned to the…
Muonic molecular ions $^6$Li$^{3+}d\mu$ and $^7$Li$^{3+}d\mu$ are studied numerically. Using the complex coordinate rotation method we found six rotational states (three for each isotope), which are resonant states with the life-time of an…
The description of the electron wavefunctions in atoms is generalized to the fractional Fourier series. This method introduces a continuous and infinite number of chirp basis sets with linear variation of the frequency to expand the…
We apply a variational method devised for the nuclear many--body problem to the 1-dimensional Hubbard--model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single…
The bound state spectra of the doublet states in three-electron atomic systems are investigated. By using different variational expansions we determine various bound state properties in these systems. Such properties include the…
Bound-state-like wave functions are used to determine the scattering matrix corresponding to low energy $N-d$ and $p-^3$He collisions. To this end, the coupled channel form of the integral relations derived from the Kohn variational…
A simple method of variational calculations of the electronic structure of a two-electron atom/ion, primarily near the nucleus, is proposed. The method as a whole consists of a standard solution of a generalized matrix eigenvalue equation,…
For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…
Wave functions of a new functional kind have been proposed for Helium-like atoms in this work . These functions explicitly depend on interelectronic and hyperspherical coordinates. The best ground state energy for the Helium atom $…
The total energies of twenty eight bound S-, P-, D-, F-, G-, H-, and I-states in the three-electron systems Li atom and Be+ ion, respectively, are determined with the use of the Configuration Interaction (CI) with Slater orbitals and L-S…
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…
In electronic structure theory, variational methods offer a valuable paradigm for approximating electronic ground states. However, for historical reasons, this principle is mostly restricted to model chemistries in pre-defined fixed basis…
In this work, trions in two-dimensional (2D) space are studied by variational method with trial wavefunctions being constructed by linear combinations of 2D slater-type orbitals (STOs). Via this method, trion energy levels and wavefunctions…
We present a simple, robust and efficient method for varying the parameters in a many-body wave function to optimize the expectation value of the energy. The effectiveness of the method is demonstrated by optimizing the parameters in…