Related papers: Development of an approximation scheme for quasi-e…
We present a new method that accurately approximates the shell-model ground-state by products of suitable states. The optimal factors are determined by a variational principle and result from the solution of rather low-dimensional…
We introduce a hybrid high-order method for approximating the ground state of the nonlinear Gross--Pitaevskii eigenvalue problem. Optimal convergence rates are proved for the ground state approximation, as well as for the associated…
Two of the most popular quantum mechanical models of interacting fermions are compared to each other and to potentially exact solutions for a pair of contact-interacting fermions trapped in a 1D double-well potential, a model of atoms in a…
Quantum computing is increasingly offering concrete solutions toward the simulation of nuclear structure, with the potential to overcome the exponential scaling that limits classical diagonalization methods in large spaces. A particularly…
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
We introduce a method for treating soft modes within the analytical framework of the quasiharmonic equation of state. The corresponding double-well energy-displacement relation is fitted to a functional form that is harmonic in both the…
The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward…
It is proven that the exact excited-state wave function and energy may be obtained by minimizing the energy expectation value of trial wave functions that are constrained only to have the correct nodes of the state of interest. This…
Highly excited vibrational states of an isolated molecule encode the vibrational energy flow pathways in the molecule. Recent studies have had spectacular success in understanding the nature of the excited states mainly due to the extensive…
The relation between the Wilson-Polchinski and the Litim optimized ERGEs in the local potential approximation is studied with high accuracy using two different analytical approaches based on a field expansion: a recently proposed genuine…
A method for approximate solution of spectral problems for Sturm-Liouville equations based on the construction of the Delsarte transmutation operators is presented. In fact the problem of numerical approximation of solutions and eigenvalues…
We investigate complex PT-symmetric potentials, associated with quasi-exactly solvable non-hermitian models involving polynomials and a class of rational functions. We also look for special solutions of intertwining relations of SUSY…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
Embedding calculations that find approximate solutions to the Schr\"{o}dinger equation for large molecules and realistic solids are performed commonly in a three step procedure involving (i) construction of a model system with effective…
A new two-parameter family of quasi-exactly solvable quartic polynomial potentials $V(x)=-x^4+2iax^3+(a^2-2b)x^2+2i(ab-J)x$ is introduced. Until now, it was believed that the lowest-degree one-dimensional quasi-exactly solvable polynomial…
We consider the solution of a generalized Exe Jahn-Teller Hamiltonian in the context of quasi-exactly solvable spectral problems. This Hamiltonian is expressed in terms of the generators of the osp(2,2) Lie algebra. Analytical expressions…
We present a procedure to solve the Schroedinger equation of two interacting electrons in a quantum dot in the presence of an external magnetic field within the context of quasi-exactly-solvable spectral problems. We show that the…
We revisit quantum phase estimation algorithms for the purpose of obtaining the energy levels of many-body Hamiltonians and pay particular attention to the statistical analysis of their outputs. We introduce the mean phase direction of the…
Early work extending the Kohn-Sham theory to excited states utilized an ensemble average of the Hamiltonian considered as a functional of the corresponding average density. We propose and develop an alternative that utilizes the matrix…
This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation…