Consequences of the Schrödinger equation for atomic and molecular physics

Clive W. Kilmister

1. Introduction C. W. Kilmister 2. Boltzmann's influence on Schrodinger Dieter Flamm 3. Schrodinger's original interpretation of the Schrodinger equation: a rescue attempt Jon Dorling 4. Are there quantum jumps? J. S. Bell 5. Square root of minus one, complex phases and Erwin Schrodinger Chen Ning Yung 6. Consequences of the Schrodinger equation for atomic and molecular physics W. E. Thirring 7. Molecular dynamics: from H + H, to biomolecules Martin Karplus 8. Orbital presentation of chemical reactions Kenichi Fukui 9. Quantum chemistry A. D. Buckingham 10. Eamon de Valera, Erwin Schrodinger and the Dublin Institute Sir William McCrea 11. Do bosons condense? J. T. Lewis 12. Schrodinger's nonlinear optics James McConnell 13. Schrodinger's unified field theory seen 40 years later O. Hittmair 14. The Schrodinger equation of the Universe S. W. Hawking 15. Overview of particle physics A. Salam 16. Gauge fields, topological defects and cosmology T. W. B. Kibble 17. Quantum theory and astronomy M. J. Seaton 18. Schrodinger's contributions to chemistry and biology Linus Pawling 19. Erwin Schrodinger's What is Life? and molecular biology M. F. Perutz.

Salvatore Capozzıello, Wladimir-Georges Boskoff

J. Weiner, Frederico Dias Nunes

This chapter begins with a discussion of radiation by a microscopic classical oscillator with radiative damping. It then turns to the Schrödinger equation for the hydrogen atom, and an extended analysis of the solutions to the Schrödinger equation for the hydrogen atom in polar coordinates is then presented. Real orbitals are constructed from linear combinations of the complex Schrödinger equation solutions. The significance of real orbitals for molecular structure and the consequent introduction of rotating and vibrating dipoles are then introduced. A semiclassical model (quantal atom and classical E-M field) for the absorption and emission of radiation is developed and compared to the Einstein A and B coefficients. It is shown how the time-dependence of the radiatively coupled non-stationary states of the hydrogen atom are analogous to the classical harmonic oscillator. The essentials of atomic transitions, as well as molecular rotational, vibrational, and electronic spectroscopy complete the chapter.

S. Rajasekar, R. Velusamy

The starting point in a quantum mechanical problem is the construction of a Schrödinger equation. We try to solve it exactly to obtain wave function. A Schrödinger equation is exactly solvable only for a certain number of simple potentials. In most of the cases the Schrödinger equation cannot be solved exactly. The solution of the Schrödinger equation for the real systems is usually complicated and often exact solutions are very difficult to find or solutions not exist. Examples include as anharmonic oscillator, hydrogen atom in an electric field, a plane rotator in the presence of an applied electric field and so on. Therefore, we need to rely on approximation methods. The simple and most interesting and powerful approximate method is the perturbation theory developed by Schrödinger in 1926 [1]. Earlier Lord Rayleigh [2] analysed harmonic vibrations of a string perturbed by small inhomogeneities. The work of Rayleigh was pointed out by Schrödinger. Consequently, the method is also called Rayleigh-Schrödinger perturbation theory. This method is powerful for determining the changes in the discrete energy values and the associated eigenfunctions of a system due to a weak perturbation, provided the eigenpairs of the undisturbed system are available. The approximations obtained from the perturbation theory are used to calculate energy level diagrams and to understand the splitting and assignments of atomic and molecular spectra [35]. The perturbation theory has been proven to be useful in several fields of theoretical physics and also in chemistry. It provides considerable insight into various phenomena. The main disadvantage of this method is that in certain problems the perturbation series converges slowly or diverges.

Lucjan Piela