相关论文: Determination of a Wave Function Functional

Standard derivations of ``time-independent perturbation theory'' of quantum mechanics cannot be applied to the general case where potentials are energy dependent or where the inverse free Green function is a non-linear function of energy.…

A variational Perturbation theory based on the functional integral approach is formulated for many-particle systems. Using the variational action obtained through Jensen-Peierls' inequality, a perturbative expansion scheme for the…

We are concerned with the problem of detecting with high probability whether a wave function has collapsed or not, in the following framework: A quantum system with a $d$-dimensional Hilbert space is initially in state $\psi$; with…

A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation…

Density Functional Theory's Kohn-Sham (KS) potential emerges as the minimizing effective potential in an unconstrained variational scheme that does not involve fixing the unknown single-electron density. The physical content behind the…

The maximum (or minimum) generalized eigenvalue of symmetric positive semidefinite matrices that depend on optimization variables often appears as objective or constraint functions in structural topology optimization when we consider…

A novel concept of multiconfigurational self-consistent field method, the generalized occupation-restricted-multiple-active-space (GORMAS) is presented. GORMAS wave functions are defined by substituting the complete active space (CAS) in…

A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…

The calculation of the band-gap by density-functional theory (DFT) methods is examined by considering the behavior of the energy as a function of number of electrons. It is found that the incorrect band-gap prediction with most approximate…

A geometric setup for constrained variational calculus is presented. The analysis deals with the study of the extremals of an action functional defined on piecewise differentiable curves, subject to differentiable, non-holonomic…

Recently, through a unified gradient flow perspective of Markov chain Monte Carlo (MCMC) and variational inference (VI), particle-based variational inference methods (ParVIs) have been proposed that tend to combine the best of both worlds.…

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-…

We propose a framework for the design and analysis of optimization algorithms in variational quantum Monte Carlo, drawing on geometric insights into the corresponding function space. The framework translates infinite-dimensional…

Variational wave functions used in the variational Monte Carlo (VMC) method are extensively improved to overcome the biases coming from the assumed variational form of the wave functions. We construct a highly generalized variational form…

The optimization of neural wave functions in variational Monte Carlo crucially relies on a robust convergence criterion. While the energy variance is theoretically a definitive measure, its practical application as a primary convergence…

Power systems are undergoing unprecedented transformations with the incorporation of larger amounts of renewable energy sources, distributed generation and demand response. All these changes, while potentially making power grids more…

The pseudospectral method is a powerful tool for finding highly precise solutions of Schr\"{o}dinger's equation for few-electron problems. We extend the method's scope to wave functions with non-zero angular momentum and test it on several…

We investigate the performance of a class of compact and systematically improvable Jastrow-Slater wave functions for the efficient and accurate computation of structural properties, where the determinantal component is expanded with a…

Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to…

The determination of an unknown spacewice dependent force function acting on a vibrating string from over-specified Cauchy boundary data is investigated numerically using the boundary element method (BEM) combined with a regularized method…