Related papers: Matrix mechanics for actual atoms and molecules
A rigorous quantum description of molecular dynamics with a particular emphasis on internal observables is developed accounting explicitly for kinetic couplings between nuclei and electrons. Rotational modes are treated in a genuinely…
We discuss the action principle and resulting Hamiltonian equations of motion for a class of integer-valued cellular automata introduced recently [1]. Employing sampling theory, these deterministic finite-difference equations are mapped…
In a cold atom gas subject to a 2D spin-dependent optical lattice potential with hexagonal symmetry, trapped atoms undergo orbital motion around the potential minima. Such atoms are elementary quantum rotors. We develop the theory of such…
We present a method for treatment of three charged particles. The proposed method has universal character and is applicable both for bound and continuum states. A finite rank approximation is used for Coulomb potential in three-body system…
Methods for calculating lower bounds to the exact energy using the variance of the upper bound energy are discussed and explored. All the matrix elements of the Hamiltonian squared are collected and considered, and those for which no known…
We construct explicit bound state wave functions and bound state energies for certain $N$--body Hamiltonians in one dimension that are analogous to $N$--electron Hamiltonians for (three-dimensional) atoms and monatomic ions.
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 study a quantum mechanical system consisting of up to three identical dipoles confined to move along a helical shaped trap. The long-range interactions between particles confined to move in this one dimension leads to an interesting…
We present a study of systems of single-molecule magnets using a semiclassical analysis and catastrophe theory. Separatrices in parameter space are constructed which are useful to determine the structure of the Hamiltonians energy levels.…
Quantum embedding theories are promising approaches to investigate strongly-correlated electronic states of active regions of large-scale molecular or condensed systems. Notable examples are spin defects in semiconductors and insulators. We…
We use atomic spectra to extend pure Coulomb's law tests to larger masses. We interpret these results in terms of constraints for hidden sector photons. With existing data the bounds for hidden photons are not improved. However we find that…
In order to understand the orbital and spin magnetization of a confined electronic system we analyze these ground state properties in the transition from a quantum dot to a quantum ring of finite thickness. The Coulomb interaction between…
We consider an Hamiltonian with ultraviolet and infrared cutoffs, describing the interaction of relativistic electrons and positrons in the Coulomb potential with photons in Coulomb gauge. The interaction includes both interaction of the…
We study a matrix product state (MPS) algorithm to approximate excited states of translationally invariant quantum spin systems with periodic boundary conditions. By means of a momentum eigenstate ansatz generalizing the one of \"Ostlund…
We illustrate Heisenberg's method of matrix mechanics using the planar quantum rotor example. We show how to find the spectrum of this simple model without the need to use the eigenstates of the system. This then leads us to speculate on…
The analytic structure of the S-matrix of singular quantum mechanics is examined within a multichannel framework, with primary focus on its dependence with respect to a parameter ($\Omega$) that determines the boundary conditions.…
We use a simple system, the electron configuration in a Hydrogen-like atom, to demonstrate the importance of using a complete basis set to provide a proper quantum mechanical description. We first start with what might be considered a…
We study the states of one and two atoms in a rotating ring lattice in a Hubbard type tight-binding model. The model is developed carefully from basic principles in order to properly identify the physical observables. The one-particle…
Starting from the random phase approximation for the weakly coupled multiband tightly-bounded electron systems, we calculate the dielectric matrix in terms of intraband and interband transitions. The advantages of this representation with…
The matrix product state formalism is used to simulate Hamiltonian lattice gauge theories. To this end, we define matrix product state manifolds which are manifestly gauge invariant. As an application, we study 1+1 dimensional one flavour…