Related papers: On Factorization of Molecular Wavefunctions
The Born-Oppenheimer electronic wavefunction $\Phi_R^{BO}(r)$ picks up a topological phase factor $\pm 1$, a special case of Berry phase, when it is transported around a conical intersection of two adiabatic potential energy surfaces in…
We combine the recently developed many-body Green's function theory for electrons and nuclei with the exact factorization of the wave function. The existing Born-Oppenheimer Green's functions are shown to be special cases of our exact…
We study the homogenization of a stochastic Schr\"odinger equation with a large periodic potential in solid state physics. Denoting by $\varepsilon$ the period, the potential is scaled as $\varepsilon^{-2}$. Under a generic assumption on…
We show that electronic wave functions Psi of atoms and molecules have a representation Psi=F*phi, where F is an explicit universal factor, locally Lipschitz, and independent of the eigenvalue and the solution Psi itself, and phi has…
The exact factorization approach, originally developed for electron-nuclear dynamics, is extended to light-matter interactions within the dipole approximation. This allows for a Schrodinger equation for the photonic wavefunction, in which…
Following Max Planck's hypothesis of quanta (quant-ph/0012069) and the matter wave idea of Louis de Broglie (quant-ph/9911107), Erwin Schroedinger proposed, at the beginning of 1926, the concept of wavefunction and wave equation for it.…
We analyze the properties that manifest Hamiltonian nature of the Schr\"odinger equation and show that it can be considered as originating from singular Lagrangian action (with two second class constraints presented in the Hamiltonian…
In 1960 Schwinger [J. Schwinger, Proc.Natl.Acad.Sci. 46 (1960) 570- 579] proposed the algorithm for factorization of unitary operators in the finite M dimensional Hilbert space according to a coprime decomposition of M. Using a special…
A many-body wave function is approximated by a product of two functions: the wave function $\phi$ depending on the particle coordinates and the function $\chi$ depending only on the value of interparticle interaction potential. For the…
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…
The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…
The approximation of the eigenvalues and eigenfunctions of an elliptic operator is a key computational task in many areas of applied mathematics and computational physics. An important case, especially in quantum physics, is the computation…
We continue studying the problem of analytic approximation of matrix functions. We introduce the notion of a partial canonical factorization of a badly approximable matrix function $\Phi$ and the notion of a canonical factorization of a…
The factorization method of Schrodinger shows us how to determine the energy eigenstates without needing to determine the wavefunctions in position or momentum space. A strategy to convert the energy eigenstates to wavefunctions is well…
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)…
This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact…
The coordinate-space wave function $\psi(x)$ of quasi-one-dimensional atoms is defined in the $x\geq 0$ region only. This poses a typical problem to write a physically acceptable momentum-space wave function $\phi(p)$ from the Fourier…
Electromagnetic phenomena can be described by Maxwell equations written for the vectors of electric and magnetic field. Equivalently, electrodynamics can be reformulated in terms of an electromagnetic vector potential. We demonstrate that…
The ground state energy of a system of electrons and nuclei is proven to be a variational functional of the conditional electronic density $n_R(\mathbf{r})$, the nuclear wavefunction $\chi(R)$ and an induced vector potential $A_{\mu}(R)$…
Fromager and Lasorne [Electron. Struct. 6 025002 (2024)] have recently derived an in-principle exact Kohn-Sham density functional theory (KS-DFT) of electrons and nuclei, where the nuclear density and the (so-called conditional) electronic…