Continuum discretization using orthogonal polynomials
A method for discretizing the continuum by using a transformed harmonic oscillator basis has recently been presented @Phys. Rev. A 63, 052111 ~2001!#. In the present paper, we propose a generalization of that formalism which does not rely on the harmonic oscillator for the inclusion of the continuum in the study of weakly bound systems. In particular, we construct wave functions that represent the continuum by making use of families of orthogonal polynomials whose weight function is the square of the ground state wave function, expressed in terms of a suitably scaled variable. As an illustration, the formalism is applied to one-dimensional ‘
An approach to the study of the continuum effects in systems of interacting Morse oscillators
An algebraic approach to the study of the continuum effects described by interacting Morse oscillators is presented. In particular, two interacting Morse oscillators are studied using the direct product of a complete basis for each Morse oscillator. We start by considering the Hamiltonian for two Morse oscillators, taking interactions up to quadratic order in both the momenta and the coordinates. The diagonalization is first carried out in the basis of the direct product of bound Morse functions for each oscillator, and thereafter using a discrete complete basis. This allows the continuum effect to be taken into account through a discretization of the continuum space. Energies, wave function characteristics, probability densities and transition intensities are studied as the dimension of the basis is increased.
Strategies for glass based photonic system integration
There is a clear tendency to integrate more and more opto-electronic and micro-optical components like optical fibers, laser diodes, modulators, isolators, beam-splitting components and micro lenses in also increasingly dense and complex assemblies. The paper will discuss thin glass as a very promising base material for that kind of photonic packaging on interposer and board level including optical interconnection using fibers.