In this paper we address again the issue of the scale anomaly in quantum mechanical models with inverse square potential. In particular we examine the interplay between the classical and quantum aspects of the system using in both cases an operatorial approach.

In particular, there have been studies within Supersymmetric Quantum Mechanics formalism. Cooper et al, [6], for instance, investigated the relationship between shape invariance and exactly analytical solvable potentials and showed that the Natanzon potential is not shape invariant although it has analytical solutions for the associated Schr odinger equation. L evai et al, [7], have determined...

We take the first nontrivial coefficient of the Schwinger-DeWitt expansion as a leading correction to the action of the second-derivative metric-dilaton gravity. To fix the ambiguities related with an arbitrary choice of the gauge fixing condition and the parametrization for the quantum field, one has to use the classical equations of motion. As a result, the only corrections are the ones to th...

We derive general relativity (GR) from a five dimensional Chern-Simons theory defined on a manifold with a boundary. The underlying mechanism is not a Kaluza-Klein reduction, rather, GR appears as an effective theory at the (four dimensional) boundary. It has been suggested many times that general relativity (GR) may not be a fundamental theory but only an effective theory arising from a still ...

To begin this activity we will explore the properties of the wave function for an electron in a simple potential energy situation. Start the Quantum Tunneling program. Go to File/ Open in the top pull-down menu and open the file Step.txt. The top half of the program screen displays a potential energy diagram similar to the one in Figure 1. This potential energy diagram is very similar to the on...

We study the static quantum potential for a theory of anti-symmetric tensor fields that results from the condensation of topological defects, within the framework of the gauge-invariant but path-dependent variables formalism. Our calculations show that the interaction energy is the sum of a Yukawa and a linear potentials, leading to the confinement of static probe charges.

We derive the correction due to noncommutativity of space on Born approximation, then the correction for the case of Yukawa potential is explicitly calculated. The correction depends on the angle of scattering. Using partial wave method it is shown that the conservation of the number of particles in elastic scattering is also valid in noncommutative spaces which means that the unitarity relatio...

At the minisuperspace level of homogeneous models, the bare probability for a classical universe has a huge peak at small universes for the Hartle-Hawking`no-boundary' wavefunction, in contrast to the suppression at small universes for thètunneling' wavefunction. If the probability distribution is cut oo at the Planck density (say), this suggests that the former quantum state is inconsistent wi...

By invoking supersymmetry, we found a condition under which the Stark-effect problem for a polar and polarizable molecule subject to nonresonant electric fields becomes exactly solvable for the |J̃ = m,m〉 family of stretched states. The analytic expressions for the wave function and eigenenergy and other expectation values allow one to readily reverse-engineer the problem of finding the values o...

The N-(2-benzoyl-phenyl) oxalyl derivatives are important models for studying of three-centered intramolecular hydrogen bonding in organic molecules. The quantum theoretical calculations for two crystal structures of N-(2-benzoyl-phenyl) oxalyl (compounds I and II) were performed by Density Functional Theory (B3LYP method and 6-311+G* basis set). From the optimized structures, geometric paramet...