Narrow Results

The classical limit of wave quantum mechanics is analyzed. It is shown that the basic requirements of continuity and finiteness to the solution of the form ψ(x) = Ae^{i ϕ (x)} + Be^{-i ϕ (x)}, where and W(x) is the reduced classical action of the physical system, give the asymptote of the wave equation and general quantization condition for the action W(x), which yields the exact eigenvalues of the system.

In response to a recently published protocol for classical teleportation of classical states [1], Hrasko [2] has made some remarks in connection with the impossibility of precise quantum teleportation if a classical mixture is used in place of the EPR state, and with regard to the epistemological interpretation of quantum states. The purpose of this note is to attempt to clarify these issues and their relevance for the argumentation presented in [1].

In this paper, a mixed quantum-classical semi-rigid vibrating rotor target (QC-SVRT) model has been applied to study the reaction O(³P) + CH₄ → CH₃ + OH based on H + CH₄ potential surface of Jordan and Gilbert. In this approach, the relative translational motion between atom and polyatom molecules is treated classically while the others are treated quantum mechanically. The reaction probabilities and rate constants were carried out using the QC-SVRT approach. It was found that the QC-SVRT results are in good agreement with the quantum results and the reaction threshold is correctly produced in the present calculation. The application of this QC-SVRT approach makes it more practical to extend quantum reaction dynamics calculation to larger molecules and more complex systems without incurring significant loss of important quantum effects.

In this chapter, the anomalous behavior of the radon data generated in a soil chamber is investigated by estimating an interval band using an interval-midpoint approach. Further, the mathematical formulation of radon transport from soil to buildings in an uncertain environment is also investigated. For the validation of the obtained results, we have used the deterministic results of the considered model problems and found good agreement between the results.

In response to a recently published protocol for classical teleportation of classical states [1], Hrasko [2] has made some remarks in connection with the impossibility of precise quantum teleportation if a classical mixture is used in place of the EPR state, and with regard to the epistemological interpretation of quantum states. The purpose of this note is to attempt to clarify these issues and their relevance for the argumentation presented in [1].

A traditional method of finding topological invariants of a knot in 3-dimensional euclidean space is to colour the arcs of a planar diagram and use this to extract invariants of the knot such as the fundamental group. This method can be extended in many ways to other kinds of codimension 2 embeddings. Moreover the new algebraic objects which arise quite naturally from these generalisations such as quandles, racks, biquandles etc are of interest in their own right. In this paper we shall give a brief overview of the methods and the new algebraic structures.