Related papers: Quantum Mechanics of a Simulated Tri-hydrogen Dica…
The electronic Schr\"odinger equation describes the motion of $N$ electrons under Coulomb interaction forces in a field of clamped nuclei. It is proved that its solutions for eigenvalues below the essential spectrum lie in the spectral…
We proposed a distributed approximating functional method for efficiently describing the electronic dynamics in atoms and molecules in the presence of the Coulomb singularities, using the kernel of a grid representation derived by using the…
Starting from a time-dependent Schr\"odinger equation, stationary states of 3D central potentials are obtained. An imaginary-time evolution technique coupled with the minimization of energy expectation value, subject to the orthogonality…
This work introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schr\"{o}dinger equation that operate in a…
Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and…
A nonlinear model representing the quantum harmonic oscillator on the three-dimensional spherical and hyperbolic spaces, $S_\k^3$ ($\kappa>0$) and $H_k^3$ ($\kappa<0$), is studied. The curvature $\k$ is considered as a parameter and then…
We develop a model of molecular binding based on the Bohr-Sommerfeld description of atoms together with a constraint taken from conventional quantum mechanics. The model can describe the binding energy curves of H2, H3 and other molecules…
We study aspects of the quantum and classical dynamics of a $3$-body system in 3D space with interaction depending only on mutual distances. The study is restricted to solutions in the space of relative motion which are functions of mutual…
An approximate method for solving the rate equations for the hydrogen populations was extended and implemented in the three-dimensional radiation (magneto-)hydrodynamics code CO5BOLD. The method is based on a model atom with six energy…
The Schr\"{o}dinger equation and ladder operators for the harmonic oscillator are shown to simplify through the use of an isometric conformal transformation. These results are discussed in relation to the Bargmann representation. It is…
When numerically simulating the unitary time evolution of an infinite-dimensional quantum system, one is usually led to treat the Hamiltonian $H$ as an "infinite-dimensional matrix" by expressing it in some orthonormal basis of the Hilbert…
We present a general framework for simulating quantum systems in the Heisenberg picture on quantum hardware. Based on the vectorization map, our framework fully exploits the mapping between operators and quantum states, allowing any task…
Solution of the momentum space Schr\"odinger equation in the case of deformed fields is being addressed. In particular it is shown that a complete set of single particle states which includes bound, resonant and complex continuum states may…
Uniqueness and reconstruction in the three-dimensional Calder\'on inverse conductivity problem can be reduced to the study of the inverse boundary problem for Schr\"odinger operators $-\Delta +q $. We study the Born approximation of $q$ in…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
A new theoretical approach to the description of the attosecond streaking measurements of atomic photoionization is presented. It is a fully quantum mechanical description based on numerical solving of the time-dependent Schroedinger…
It is shown that the molecular ion ${\rm H}^{++}_3$ does not exist in a form of the equilateral triangle. To this end, a compact variational method is presented which is based on a linear superposition of six specially tailored trial…
In this study, we present analytical solutions of the Schr\"odinger equation with the Multiparameter potential containing the different types of physical potential via the asymptotic iteration method (AIM) by applying a Pekeris-type…
We use variable transformation from the real line to finite or semi-infinite spaces where we expand the regular solution of the 1D time-independent Schrodinger equation in terms of square integrable bases. We also require that the basis…
We present a new fast algorithm which allows the simulation of ionising radiation emitted from point sources to be included in high-resolution three-dimensional smoothed particle hydrodynamics simulations of star cluster formation. We…