Related papers: Calculation of Hydrogenic Bethe Logarithms for Ryd…
Computational Fluid Dynamics simulations are crucial in industrial applications but require extensive computational resources, particularly for extreme turbulent regimes. While classical digital approaches remain the standard, quantum…
Solving the electronic Schrodinger equation for strongly correlated ground states is a long-standing challenge. We present quantum algorithms for the variational optimization of wavefunctions correlated by products of unitary operators,…
There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful classical numerical approach to obtain ground states. However, most of the proposals so far require heavy post-processing…
Expectation values of powers of the radial coordinate in arbitrary hydrogen states are given, in the quantum case, by an integral involving the associated Laguerre function. The method of brackets is used to evaluate the integral in…
The search for signals of new physics at the forthcoming LHC experiments involves the analysis of final states characterised by a high number of hadronic jets or identified particles. Precise theoretical predictions for these processes…
Fully numerical mesh solutions of 2D quantum equations of Schroedinger and Hartree-Fock type allow us to work with wavefunctions which possess a very flexible geometry. This flexibility is especially important for calculations of atoms and…
Elements are given of a calculation that identifies the size of a proton in the Schroedinger equation for lepton-proton bound states, using the renormalization group procedure for effective particles (RGPEP) in quantum field theory,…
We examine the performance of various time propagation schemes using a one-dimensional model of the hydrogen atom. In this model the exact Coulomb potential is replaced by a soft-core interaction. The model has been shown to be a reasonable…
We present a regularized finite difference method for the logarithmic Schr\"odinger equation (LogSE) and establish its error bound. Due to the blow-up of the logarithmic nonlinearity, i.e. $\ln \rho\to -\infty$ when $\rho\rightarrow 0^+$…
The two-loop self-energy correction to the ground state Lamb shift is calculated for hydrogen-like ions with the nuclear charge Z=10-30 without any expansion in the binding field of the nucleus. A calculational technique is reported for…
Since a pure quantum system is incapable of faithfully simulating the solutions of the Schroedinger equation that actually pertains to itself, it is proposed that quantum computing technology (as opposed to cryptographic technology) not be…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
The dynamics of vortex solitons in a BEC superfluid is studied. A quantum lattice-gas algorithm (localization-based quantum computation) is employed to examine the dynamical behavior of vortex soliton solutions of the Gross-Pitaevskii…
The Kepler-Coulomb problem is solved in parabolic coordinates and the Larmor radiation problem is analyzed to complement a previous study performed for the usual representation in spherical polar coordinates. A comparison with quantum…
A square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, extended to include the effects of solvent quality, is examined in the framework of the Bethe approximation.
We present a numerical analysis of the validity of classical and generalized hydrodynamics for Lattice Boltzmann Equation (LBE) and Lattice BGK methods in two and three dimensions, as a function of the collision parameters of these models.…
We present an improved calculation of higher-order corrections to the one-loop self energy of 2P states in hydrogen-like systems with small nuclear charge Z. The method is based on a division of the integration with respect to the photon…
Hylleraas in 1929 carried out a variational computation on the Schrodinger equation for the helium atom which gave, for the first time, a ground-state energy in essential agreement with experimental results. Coolidge and James in 1933,…
We consider the feasibility of studying the anisotropic Heisenberg quantum spin chain with the Variational Quantum Eigensolver (VQE) algorithm, by treating Bethe states as variational states, and Bethe roots as variational parameters. For…
Tunnel ionization rates of triplet Rydberg states in helium with principal quantum numbers close to 37 have been measured in electric fields at the classical ionization threshold of $\sim197$ V/cm. The measurements were performed in the…