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 ‘
Systematic calculation of molecular vibrational spectra through a complete Morse expansion
We propose an accurate and efficient method to compute vibrational spectra of molecules, based on exact diagonalization of an algebraically calculated matrix based on powers of Morse coordinate. The present work focuses on the 1D potential of diatomic molecules: as typical examples, we apply this method to the standard Lennard-Jones oscillator, and to the ab initio potential of the H2 molecule. Global cm−1 accuracy is exhibited through the H2 spectrum, obtained through the diagonalization of a 30 × 30 matrix. This theory is at the root of a new method to obtain globally accurate vibrational spectral data in the context of the multi-dimensional potential of polyatomic molecules, at an affordable computational cost. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007
Commentary: Scholarship as a Way of Life—Character and Virtue in the Age of Big Humanities
From the Renaissance to the nineteenth century, most European scholars considered moral cultivation as the primary purpose of the humanities. The humanities were human not just because they concerned the products of the human mind but also because they transformed scholars and students into better human beings. During the late nineteenth and early twentieth centuries, the rise of Big Humanities questioned this moral purpose. However, Big Humanities also reemphasized the importance of epistemic virtues for scholarship. The language of epistemic virtues helped scholars create new communities of learning and scholarship. Within these communities, the language of virtues established common standards of collaboration and granted scholars a sense of purpose. Many of these scholars also continued to associate epistemic virtues with moral virtues.