Three Electrons in a Two-Dimensional Parabolic Trap: The Relative Motion Solution

In agreement with the Kohn theorem the relative motion (rel) of three electrons in a two-dimensional parabolic trap separates from the centre-of-mass (CM) motion. By introducing new coordinates the Hamiltonian for relative motion in the approximation of non-interacting electrons can be taken to the normal form. The eigenstates of the normalized Hamiltonian are products of the Fock-Darwin states for normal modes. The energy levels for relative motion are obtained by diagonalizing the exact Hamiltonian in the eigenbasis for the non-interacting case. In this basis the interaction matrix elements can be obtained in the analytical form. Since the rank of the Hamiltonian matrix is significantly reduced, the calculations are faster and more accurate than those for the full (CM + rel) motion. This advantage is especially important for the calculations of excited states and the analysis of energy spectra.     

Dendrimers as scaffolds for multifunctional reversible addition–fragmentation chain transfer agents: Syntheses and polymerization

The synthesis and characterization of novel first‐ and second‐generation true dendritic reversible addition–fragmentation chain transfer (RAFT) agents carrying 6 or 12 pendant 3‐benzylsulfanylthiocarbonylsulfanylpropionic acid RAFT end groups with Z‐group architecture based on 1,1,1‐hydroxyphenyl ethane and trimethylolpropane cores are described in detail. The multifunctional dendritic RAFT agents have been used to prepare star polymers of poly(butyl acrylate) (PBA) and polystyrene (PS) of narrow polydispersities (1.4 < polydispersity index < 1.1 for PBA and 1.5 < polydispersity index < 1.3 for PS) via bulk free‐radical polymerization at 60 °C. The novel dendrimer‐based multifunctional RAFT agents effect an efficient living polymerization process, as evidenced by the linear evolution of the number‐average molecular weight (M_n) with the monomer–polymer conversion, yielding star polymers with molecular weights of up to M_n = 160,000 g mol^?1 for PBA (based on a linear PBA calibration) and up to M_n = 70,000 g mol^?1 for PS (based on a linear PS calibration). A structural change in the chemical nature of the dendritic core (i.e., 1,1,1‐hydroxyphenyl ethane vs trimethylolpropane) has no influence on the observed molecular weight distributions. The star‐shaped structure of the generated polymers has been confirmed through the cleavage of the pendant arms off the core of the star‐shaped polymeric materials. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 5877–5890, 2004     

Quantum Interference, Quantum Theory of Measurement, and (In)completeness of Quantum Mechanics

The new techniques and ideas in quantum interferometry with neutrons, photons, atoms, electrons, and Bose condensates that fluorished in the last two decades have influenced in a decisive way the thinking and the research in the foundations and interpretation of quantum mechanics. The controversies existing among different schools on the reality of matter waves of quantum theory, the postulates of quantum measurement theory, and the (in)completeness of quantum mechanics have to be approached now in a new way. Our argumentation follows the spirit of the Paris school.