Related papers: Wronskian method and the Schr\"odinger eigenvalue …
In the present work, we studied the q-deformed Morse and harmonic oscillator systems with appropriate canonical commutation algebra. The analytic solutions for eigenfunctions and energy eigenvalues are worked out using time-independent…
We represent low dimensional quantum mechanical Hamiltonians by moderately sized finite matrices that reproduce the lowest O(10) boundstate energies and wave functions to machine precision. The method extends also to Hamiltonians that are…
By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining…
The molecular Schr\"odinger equation is rewritten in terms of non-unitary equations of motion for the nuclei (or electrons) that depend parametrically on the configuration of an ensemble of generally defined electronic (or nuclear)…
We study two seminal approaches, developed by B. Simon and J. Kisy\'nski, to the well-posedness of the Schr\"odinger equation with a time-dependent Hamiltonian. In both cases the Hamiltonian is assumed to be semibounded from below and to…
We use Wegner's flow equation method to investigate the infinite-$U$ periodic Anderson model. We show that this method poses a new approach to the description of heavy fermion behaviour. Within this scheme we derive an effective Hamiltonian…
Free energy calculations based on atomistic Hamiltonians and sampling are key to a first principles understanding of biomolecular processes, material properties, and macromolecular chemistry. Here, we generalize the Free Energy Perturbation…
The implementation of an efficient self-consistent field (SCF) method including both scalar relativistic effects and spin-orbit interaction in density functional theory (DFT) is presented. We make use of Gaussian-type orbitals (GTOs) and…
We consider the numerical evaluation of the Evans function, a Wronskian-like determinant that arises in the study of the stability of travelling waves. Constructing the Evans function involves matching the solutions of a linear ordinary…
Classical equations of motion that are first-order in time and conserve energy can only be quantized after their variables have been transformed to canonical ones, i.e., variables in which the energy is the system's Hamiltonian. The…
The nonlinear Schr\"odinger and the Schr\"odinger-Newton equations model many phenomena in various fields. Here, we perform an extensive numerical comparison between splitting methods (often employed to numerically solve these equations)…
Heavy quarkonia, Bc-meson, and CS-meson masses are calculated within the framework of the N-dimensional radial Schrodinger equation. The Cornell potential is extended by including the harmonic oscillator potential. The energy eigenvalues…
We prove a weighted Carleman estimate for a class of one-dimensional, self-adjoint Schr\"odinger operators $P(h)$ with low regularity electric and magnetic potentials, where $h > 0$ is a semiclassical parameter. The long range part of…
The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…
We study the one-dimensional Schr\"odinger equation and derive exact expressions for the Green function in terms of reflection coefficients which are defined for semi-infinite intervals. We also discuss the relation between our results and…
This paper presents the multi-channel generalization of the center-of-mass kinetic energy elimination approach [Mol. Phys., 111 2086 (2013)] when the Schr\"odinger equation is solved variationally with explicitly correlated Gaussian…
Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical…
We consider a coupled system of Schr\"odinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics…
In this paper, we study the time-independent Schr\"odinger equation within the formalism of position dependent effective mass. For a generalized decomposition of the non-central effective potential, the deformed Schr\"odinger equation can…
Favorably scaling numerical time-dependent many-electron techniques such as time-dependent density functional theory (TDDFT) with adiabatic exchange-correlation potentials typically fail in capturing highly correlated electron dynamics. We…