Related papers: On matrix elements of the vector physical quantiti…
We discuss the efficient computation of the auxiliary integrals that arise when resolutions of two-electron operators (specifically, the Coulomb and long-range Ewald operators) are employed in quantum chemical calculations. We derive a…
It is obvious that we still have not any unified framework covering a zoo of interpretations of Quantum Mechanics, as well as satisfactory understanding of main ingredients of a phenomena like entanglement. The starting point is an idea to…
The Hartree-Fock-Rothaan equations are solved for He-like ions using the iterative self-consistent method. New complete and orthonormal sets of exponential-type orbitals are employed as the basis. These orbitals satisfy the orthonormality…
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the…
When a hydrogen-like atom is treated as a two dimensional system whose configuration space is multiply connected, then in order to obtain the same energy spectrum as in the Bohr model the angular momentum must be half-integral.
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
The random matrix ensembles are applied to the quantum statistical two-dimensional systems of electrons. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The…
Traditional theory of many-electron atoms and ions is based on the coefficients of fractional parentage and matrix elements of tensorial operators, composed of unit tensors. Then the calculation of spin-angular coefficients of radial…
For a charge-monopole pair, though the definition of the orbital angular momentum is different from the usual one, and the transverse part of the momentum that includes the vector potential as an additive term turns out to be the so-called…
The angular momentum of molecules, or, equivalently, their rotation in three-dimensional space, is ideally suited for quantum control. Molecular angular momentum is naturally quantized, time evolution is governed by a well-known Hamiltonian…
We investigate the quark angular momentum in a model with the nucleon being a quark and a spectator. Both scalar and axial-vector spectators are included. We perform the calculations in the light-cone formalism where the parton concept is…
In a calculation of rotated matrix elements with angular momentum projection, the generalized Wick's theorem may encounter a practical problem of combinatorial complexity when the configurations have more than four quasi-particles (qps).…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
The method of McCurdy, Baertschy, and Rescigno, J. Phys. B, 37, R137 (2004) is generalized to obtain a straightforward, surprisingly accurate, and scalable numerical representation for calculating the electronic wave functions of molecules.…
Based on the novel prescription for the power of a complex number, a new expression for the eigenfunction of the operator of the third component of the angular momentum is presented. These functions are normalizable, single valued and are…
The conformability of angular observales (angular momentum and azimuthal angle) with the mathematical rules of quantum mechanics is a question which still rouses debates. It is valued negatively within the existing approaches which are…
We study QED corrections to operator matrix elements involving heavy composite particles (e.g., heavy-mesons, nuclei, and atoms). We define a new notion of reducible and irreducible graphs which is useful for systems with many discrete…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Classical transport equations with probabilistic initial conditions can be viewed as quantum systems. In a discrete version they are probabilistic automata. The time-local probabilistic information is encoded in a classical wave function.…