Related papers: Ammonia Inversion Energy Levels using Operator Alg…
An attempt has been made in this paper to modify Grover's Algorithm to find the binary string solutions approximating a target cost value. In that direction, new Controlled Oracle and the Local Diffusion Operator are suggested, apart from…
The influence of oscillating quadrupole fields on atomic energy levels is examined theoretically and general expressions for the quadrupole matrix elements are given. The results are relevant to any ion-based clock in which one of the clock…
The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are…
We apply the algebraic method to the Bateman Hamiltonian and obtain its natural frequencies and ladder operators from the adjoint or regular matrix representation of that operator. Present analysis shows that the eigenfunctions compatible…
We observe Arp 220, the nearest Ultra-Luminous Infrared Galaxy (ULIRG), over 4 GHz in the K and Ka bands. We provide constraints for the kinematics,morphology, and identify molecular species on scales resolving both nuclei (0.6" or 230 pc).…
The Fourier component of the potential energy of interaction of an atom with an atom is represented as a polynomial of the fourth degree from the atomic form factor. A numerical calculation was performed for the atomic form factor in the…
We describe electromagnetic and favored \alpha-transitions to rotational bands in odd-mass nuclei built upon a single particle state with angular momentum projection $\Omega=\frac{1}{2}$ in the region $88 \le Z \le 98$. We use the particle…
The recent high-precision measurements of alpha-particle induced reaction data below the Coulomb barrier (B) make possible the understanding of limits and possible improvement of a previous optical model potential (OMP) for alpha-particles…
We present a straightforward method for obtaining exact classical and quantum molecular Hamiltonians in terms of arbitrary coordinates. As compared to other approaches the resulting expression are rather compact, the physical meaning of…
The Uehling correction to the energy levels is presented in terms of the hypergeometric functions 2F1. This presentation allows to derived various asymptotics and approximations. Further applications of this method to other atomic…
Using first-principles only, we calculate the melting point of MgO, also called periclase or magnesia. The random phase approximation (RPA) is used to include the exact exchange as well as local and non-local many-body correlation terms, in…
We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x)^2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient…
Let $\Omega$ be an open set in $\R^d$ $(d > 1)$ and $h(\Omega)$ the Fr\'echet space of harmonic functions on $\Omega$. Given a bounded linear operator $L :h(\Omega)\to h(\Omega)$, we show that its eigenvalues $\lambda_n$, arranged in…
We present and compare three generically applicable signal processing methods for periodic orbit quantization via harmonic inversion of semiclassical recurrence functions. In a first step of each method, a band-limited decimated periodic…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
The capabilities of the functional-analytic and of the functional-integral approach for the construction of the Hamiltonian as a self-adjoint operator on Hilbert space are compared in the context of non-relativistic quantum mechanics.…
We consider a slow-fast Hamiltonian system with one fast angular variable (a fast phase) whose frequency vanishes on some surface in the space of slow variables (a resonant surface). Systems of such form appear in the study of dynamics of…
For an electron confined to a surface reconstructed by double-frequency corrugations, we give the effective Hamiltonian by the formula of geometric influences, obtain an additive scalar potential induced by curvature that consists of…
We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions…
An algebraic model based on Lie-algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. The local anharmonic effects are described by a Morse-like potential and corresponding anharmonic…