Related papers: Integrals for lower bounds to the exact energy
Within the framework of the quark model and the variational method, the bound states of four heavy quarks (tetraquarks) are investigated. The basis variational wave functions are chosen in the Gaussian form. The matrix elements of the…
For Hamiltonian systems, simulation algorithms that exactly conserve numerical energy or pseudo-energy have seen extensive investigation. Most available methods either require the iterative solution of nonlinear algebraic equations at each…
The development of computational resources has made it possible to determine upper bounds for atomic and molecular energies with high precision. Yet, error bounds to the computed energies have been available only as estimates. In this…
There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of…
Key properties of physical systems can be described by the eigenvalues of matrices that represent the system. Computational algorithms that determine the eigenvalues of these matrices exist, but they generally suffer from a loss of…
Accurate predictions for hydrogen molecular levels require the treatment of electrons and nuclei on an equal footing. While nonrelativistic theory has been effectively formulated this way, calculation of relativistic and quantum…
Exact analytical expressions for the matrix elements of the Uehling potential in a basis of explicitly correlated exponential wave functions are presented. The obtained formulas are then used to compute with an improved accuracy the vacuum…
By the use of the variational method with exponential trial functions the upper and lower bounds of energy are calculated for a number of non-relativistic three-body Coulomb and nuclear systems. The formulas for calculation of upper and…
An exact solution of the energy shift in each quantum mechanical energy levels in a one dimensional symmetrical linear harmonic oscillator has been investigated. The solution we have used here is firstly derived by manipulating Schrodinger…
We establish a procedure to find the extremal density matrices for any finite Hamiltonian of a qudit system. These extremal density matrices provide an approximate description of the energy spectra of the Hamiltonian. In the case of…
Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales…
A method is presented to compute approximate solutions for eigenequations in quantum mechanics with an arbitrary kinetic part. In some cases, the approximate eigenvalues can be analytically determined and they can be lower or upper bounds.…
We derive out a complete series expression of Hamiltonian eigenvalues without any approximation and cut in the general quantum systems based on Wang's formal framework \cite{wang1}. In particular, we then propose a calculating approach of…
We develop a quantum algorithm for estimating the free energy as well as the total Gibbs state of interacting quantum Coulomb gases and molecular systems in dimensions $d \in \{2,3\}$ at finite temperature. These systems lie beyond the…
Considering recent advancements and successes in the development of efficient quantum algorithms for electronic structure calculations --- alongside impressive results using machine learning techniques for computation --- hybridizing…
The energy levels of the ground states of the three-particle and four-particle bound states of leptons in quantum electrodynamics are calculated. For the calculation, the variational method with Gaussian basis functions is used. The…
For a wide class of Hamiltonians, a novel method to obtain lower and upper bounds for the lowest energy is presented. Unlike perturbative or variational techniques, this method does not involve the computation of any integral (a…
Linear programming (polynomial) techniques are used to obtain lower and upper bounds for the potential energy of spherical designs. This approach gives unified bounds that are valid for a large class of potential functions. Our lower bounds…
In quasi-exactly solvable problems partial analytic solution (energy spectrum and associated wavefunctions) are obtained if some potential parameters are assigned specific values. We introduce a new class in which exact solutions are…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…