Table of contents

We used an invariant operator to obtain the Schrödinger solution of damped-amplified oscillators. The expectation values of the quantum mechanical energy operator correspond to the classical energy. The geometrical phase of the system increased linearly with time. We confirmed that the uncertainty principle always holds. The uncertainty relation in coherent state is the same as the minimum value of that in number state.

The solutions of the two-dimensional Schrödinger equation with a Coulomb potential are briefly studied and compared with those of the Klein-Gordon case studied in this work. The eigenvalues and the normalized eigenfunctions are analytically obtained. The fine structure of the energy level for this system is also discussed.

It is shown that continuous classical nonlinear canonical (Poisson) maps have a distinguished role in quantum mechanics. They act unitarily on the quantum phase space and generate ℏ-independent quantum nonlinear canonical maps. It is also shown that such maps act in the non-commutative phase space under the classical covariance. A crucial result of the work is that under the action of Poisson maps a local quantum mechanical picture is converted onto a non-local picture which is then represented in a non-local Hilbert space. On the other hand, it is known that a non-local picture is equivalent by the Weyl map to a non-commutative picture which, in the context of this work, corresponds to a phase space formulation of the theory. As a result of this equivalence, a phase space Schrödinger picture can be formulated. In particular, we obtain the ⋆-genvalue equation of Fairlie (1964 Proc. Camb. Phil. Soc.60 581) and Curtright, Fairlie and Zachos (1998 Phys. Rev. D 58 025002). In a non-local picture entanglement becomes a crucial concept. The connection between the entanglement and non-locality is explored in the context of Poisson maps and specific examples of the generation of entanglement from a local wavefunction are provided by using the concept of generalized Bell states. The results obtained are also relevant for the non-commutative soliton picture in the non-commutative field theories. We elaborate on this in the context of the scalar non-commutative field theory.

We have calculated the excitation energies, oscillator strengths and transition probabilities for electric-dipole-allowed and inter-combination transitions among the lowest 25 LS levels belonging to the configurations (1s²2s²2p⁶)3s²3p(²P^o), 3s3p²(²S, ²P, ²D, ⁴P), 3s²3d(²D), 3p³(⁴S^o, ²P^o, ²D^o), 3s3p(³P^o)3d(²P^o, ²D^o, ²F^o, ⁴P^o, ⁴D^o, ⁴F^o), 3s3p(¹P^o)3d(²P^o, ²D^o, ²F^o), 3s²4s(²S), 3s²4p(²P^o), 3s²4d(²D), 3s²4f(²F^o), 3s3p(³P^o)4s(²P^o, ⁴P^o), and 3s3p(¹P^o)4s(²P^o) of P III using the Program CIV3 of Hibbert. These states are represented by extensive configuration-interaction (CI) wave functions. The radiative lifetimes of 18 doublet and 4 quartet states of P III have also been calculated from our transition probabilities. Our results are compared with experimental and other theoretical data. To assess the importance of relativistic effects on our calculated values, we have carried out calculations in the intermediate-coupling scheme using the Breit-Pauli Hamiltonian. Small adjustments to the diagonal elements of the Hamiltonian matrices have been made. The energy splittings of 54 fine-structure levels, the oscillator strengths and transition probabilities for some strong dipole-allowed and intercombination transitions and the lifetimes of some fine-structure levels are presented.

We have recorded hollow-cathode spectra of neutral vanadium by Fourier transform spectroscopy in the near infrared – visible region (9000–17 000 cm^-1). 36 transitions showing hyperfine structure have been analyzed, allowing us to deduce magnetic dipole constants for 27 levels belonging to the 3d⁴4p and 3d³4s4p configurations. For 22 of these levels no data were previously available.

Using a cubic-quintic nonlinear Schrödinger equation as a model, we study the existence and interactions of two-dimensional (2D) solitons on top of a continuous-wave background. It is shown that the 2D solitons exist in the form of dark or antidark lumps, which are described by an effective KP (Kadomtsev-Petviashvili)-I equation. Interactions and collisions of 2D solitons are investigated using both analytical and numerical techniques. The most remarkable feature of the interaction is formation of a transient long-lived quasi-bound state of two colliding solitons, before they separate.

Nonlinear equations governing the dynamics of low-frequency (in comparison with electron gyro-frequency) electrostatic disturbances in a nonuniform resistive dust-contaminated electron-positron magnetoplasma with equilibrium sheard flow are derived. In the linear limit, a local dispersion relation has been derived and analyzed. On the other hand, in the nonlinear case, the temporal behavior of the nonlinear system can be represented in the form of a 5 × 5 matrix, which is a generalization of Lorenz-Stenflo equations admitting chaotic trajectories. We have also presented a linear stability analysis of a generalized Lorenz-Stenflo system of equations under different approximations. It is also shown that for small magnetic shear and for a nondissipative plasma, a quasi-stationary solution of the mode coupling equations can be represented in the form of counter-rotating vortices. These results would be helpful to understand plasma turbulence and wave phenomena which have frequently been observed in several laboratory and astrophysical plasma systems.

The propagation of a short laser beam in plasma is investigated analytically. Relativistic ponderomotive force and space charge effects are included, and an equation describing the evolution of the laser spot size is derived. It is shown that self-consistent electron cavitation can lead to self channelling and thus long-distance self-focusing of the laser. The condition for the latter to occur is given.

In the present paper we investigate the influence of inhomogeneities in the dynamics and stability of DNA open states, modeled as propagating solitons in the spirit of a Generalized Yakushevich Model. It is a direct consequence of our model that there exists a critical distance between the soliton's center of mass and the inhomogeneity at which the interaction between them can change the stability of the open state. Further a renormalized potential function was derived from this result.

Single crystal EPR and optical studies of Cu(II) doped ZnNH₄PO₄ · 6H₂O (Zinc struvite) have been carried out at room and liquid nitrogen temperatures. The g and A tensors indicate that the impurity has entered the lattice substitutionally. Even though the coordination polyhedron around the host Zn(II) is a compressed octahedron of oxygen atoms of water, the Cu(II) ion has an elongated octahedron corresponding to d_x²-y² ground state. The optical spectrum shows four bands at 1205, 1095, 833 and 805 nm, which confirms the octahedral coordination of Cu(II) with rhombic (C_2V) distortion.

A dynamic approach is developed for the two principle phases of (i) gravitational condensation, and (ii) burning fusion plasma evolution. Comparison is made with conceptual descriptions of star formation and of subsequent decay towards red giant stars, white dwarfs, and other condensed core objects like neutron stars and black holes. The possibility of treating the expansion of the Universe by means of a similar approach is also discussed. The concept of negative diffusion is introduced for the contraction phase of star formation. The coefficients defining the nonlinear diffusion are determined uniquely by physical conditions and for the case of the expansion of the universe, by the observation of the Hubble law. The contraction and evolution of large scale 3-D stars and 2-D galactic systems can thus be dynamically surveyed. In particular the time-scales can be determined.