Quantum mechanical Liouville model with attractive potential

We study the quantum mechanical Liouville model with attractive potential which is obtained by Hamiltonian symmetry reduction from the system of a free particle on SL(2, \Real). The classical reduced system consists of a pair of Liouville subsystems which are `glued together' in such a way that the singularity of the Hamiltonian flow is regularized. It is shown that the quantum theory of this reduced system is labelled by an angle parameter $\theta \in [\,0,2\pi)$ characterizing the self-adjoint extensions of the Hamiltonian and hence the energy spectrum. There exists a probability flow between the two Liouville subsystems, demonstrating that the two subsystems are also `connected' quantum mechanically, even though all the wave functions in the Hilbert space vanish at the junction.Comment: 20 pages, plain tex, 2 Postscript figure

Correlation, Breit and Quantum Electrodynamics effects on energy level and transition properties of W54+^{54+} ion

The electron correlation effects and Breit interaction as well as Quantum Electro-Dynamics (QED) effects were expected to have important contribution to the energy level and transition properties of heavy highly charged ions. The ground states [Ne]$3s^{2}3p^{6}3d^{2}$ and first excited states [Ne]3s$^{2}3p^{5}3d^{3}$ of W$^{54+}$ ion have been studied by using Multi-Configuration Dirac-Fock method with the implementation of Grasp2K package. A restricted active space was employed to investigate the correlation contribution from different models. The Breit interaction and QED effects were taken into account in the relativistic configuration interaction calculation with the converged wavefunction. It is found that the correlation contribution from 3s and 3p orbital have important contribution to the energy level, transition wavelength and probability of the ground and the first excited state of W$^{54+}$ ion