Electron energy level crossings in the time-dependent Born-Oppenheimer approximation

Summary We summarize the results of a mathematical study of the time-dependent Born-Oppenheimer approximation near crossings of two non-degenerate electron energy surfaces. We illustrate our techniques by relatively simple examples that contain the essential ingredients of the general cases. We discuss all generic types of crossings of two non-degenerate electron energy surfaces.Supported in part by the National Science Foundation under Grant number DMS-8801360     

Mechanisiertes thermometrisches Analysenverfahren zur Bestimmung von Substanzen in weiten Konzentrationsbereichen

A procedure for mechanised thermometric analysis is described which can be used for the continuous analysis of sample streams as well as for the determination of components in individual samples. In contrast to thermometric methods of analysis previously used, this new procedure is particularly applicable for substances present in medium to high concentrations, and is therefore suitable for many industrial purposes. The analytical exploitation of enthalpy changes as for example with neutralisation, redox and precipitation reactions as well as with dilution, opens wide application possibilities. The precision of the results is generally very good.     

Elementary Exponential Error Estimates for the Adiabatic Approximation

We present an elementary proof that the quantum adiabatic approximation is correct up to exponentially small errors for Hamiltonians that depend analytically on the time variable. Our proof uses optimal truncation of a straightforward asymptotic expansion. We estimate the terms of the expansion with standard Cauchy estimates.     

A time dependent Born-Oppenheimer approximation

We consider the dynamics of a quantum mechanical system which consists of some particles with large masses and some particles with small masses. As we increase the large masses to infinity we obtain the following results: The particles of smaller mass move adiabatically and determine an effective potential in which the heavier particles move semiclassically. Our methods can be applied to diatomic molecules with Coulomb forces.Supported in part by the National Science Foundation under Grant PHY 78-08066