Related papers: Determination of Wave Function Functionals: The Co…
This paper introduces variational design methods that are novel to Geophysics, and discusses their benefits and limitations in the context of geophysical applications and more established design methods. Variational methods rely on…
The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle…
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
Given a parameterized quantum circuit such that a certain setting of these real-valued parameters corresponds to Grover's celebrated search algorithm, can a variational algorithm recover these settings and hence learn Grover's algorithm? We…
Travelling wave solutions of reaction-diffusion equations are widely used to model the spatial spread of populations and other phenomena in biology and physics. In this article, we reinterpret the classical variational principle approach…
In this article, we answer the following question: If the wave equation possesses bound states but it is exactly solvable for only a single non-zero energy, can we find all bound state solutions (energy spectrum and associated…
We present a variational method which uses a quartic exponential function as a trial wave-function to describe time-dependent quantum mechanical systems. We introduce a new physical variable $y$ which is appropriate to describe the shape of…
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 nuclear energy density functional method at finite temperature is a useful tool for studies of nuclear structure at high excitation, and also for researches of nuclear matter involved in explosive stellar phenomena and neutron stars.…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We present an approximation scheme for functions in three dimensions, that requires only their samples on the Cartesian grid, under the assumption that the functions are sufficiently concentrated in both space and frequency. The scheme is…
Recently a new class of quantum algorithms that are based on the quantum computation of the connected moment expansion has been reported to find the ground and excited state energies. In particular, the Peeters-Devreese-Soldatov (PDS)…
For fixed $c,$ Prolate Spheroidal Wave Functions (PSWFs), denoted by $\psi_{n, c},$ form an orthogonal basis with remarkable properties for the space of band-limited functions with bandwith $c$. They have been largely studied and used after…
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…
Perhaps the simplest first-principles approach to electronic structure is to fit the charge distribution of each orbital pair and use those fits wherever they appear in the entire electron-electron (EE) interaction energy. The charge…
A variational approach, based on a discrete representation of the chain, is used to calculate free energy and conformational properties in polyelectrolytes. The true bond and Coulomb potentials are approximated by a trial isotropic harmonic…
This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…
The Energy Density Functional theory is one of the most used methods developed in nuclear structure. It is based on the assumption that the energy of the ground state is a functional only of the density profile. The method is extremely…
In this work we address partial wave decompositions of thermal one-point functions in conformal field theories on $S^1 \times S^{d-1}$. With the help of Casimir differential equations we develop efficient algorithms to compute the relevant…
A one-electron Schroedinger equation based on special one-electron potentials for atoms is shown to exist that produces orbitals for an arbitrary molecule that are sufficiently accurate to be used without modification to construct single-…