The inverse of an $infty times infty$ symmetric band matrix can be constructed in terms of a matrix continued fraction. For Hamiltonians with Coulomb plus polynomial potentials, this results in an exact and analytic Greens operator which, even in fin
ite-dimensional representation, exhibits the exact spectrum. In this work we propose a finite dimensional representation for the potential operator such that it retains some information about the whole Hilbert-space representation. The potential should be represented in a larger basis, then the matrix should be inverted, then truncated to the desired size, and finally inverted again. This procedure results in a superb low-rank representation of the potential operator. The method is illustrated with a typical nucleon-nucleon potential.
The fishbone potential of composite particles simulates the Pauli effect by nonlocal terms. We determine the $n-alpha$ and $p-alpha$ fish-bone potential by simultaneously fitting to the experimental phase shifts. We found that with a double Gaussian
parametrization of the local potential can describe the $n-alpha$ and $p-alpha$ phase shifts for all partial waves.
Microstructure changes during annealing of nano-crystalline silver and amorphous silicon multilayers (Ag/a-Si) have been studied by X-ray diffraction and transmission electron microscopy. The dc-magnetron sputtered Ag/a-Si multilayers remained stable
even after annealing at 523K for 10h, and microstructural changes occurred only above 600K. The degradation of Ag/a-Si multilayers can be described by the increase of size of Ag grains, formation of grooves and pinholes at Ag grain boundaries and by the diffusion of silicon atoms through the silver grain boundaries and along the Ag/a-Si interfaces. This results in thinning of a-Si layers, and in formation of Ag granulates after longer annealing times.
Three-body resonances in atomic systems are calculated as complex-energy solutions of Faddeev-type integral equations. The homogeneous Faddeev-Merkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. T
he Coulomb-Sturmian matrix elements of the three-body Coulomb Greens operator has been calculated as a contour integral of two-body Coulomb Greens matrices. This approximation casts the integral equation into a matrix equation and the complex energies are located as the complex zeros of the Fredholm determinant. We calculated resonances of the e-Ps system at higher energies and for total angular momentum L=1 with natural and unnatural parity
Two body data alone cannot determine the potential uniquely, one needs three-body data as well. A method is presented here which simultaneously fits local or nonlocal potentials to two-body and three-body observables. The interaction of composite par
ticles, due to the Pauli effect and the indistinguishability of the constituent particles, is genuinely nonlocal. As an example, we use a Pauli-correct nonlocal fish-bone type optical model for the $alpha-alpha$ potential and derive the fitting parameters such that it reproduces the two-$alpha$ and three-$alpha$ experimental data.
In quantum mechanics with minimal length uncertainty relations the Heisenberg-Weyl algebra of the one-dimensional harmonic oscillator is a deformed SU(1,1) algebra. The eigenvalues and eigenstates are constructed algebraically and they form the infin
ite-dimensional representation of the deformed SU(1,1) algebra. Our construction is independent of prior knowledge of the exact solution of the Schrodinger equation of the model. The approach can be generalized to the $D$-dimensional oscillator with non-commuting coordinates.
