Exact Solutions of Dirac Equation on (1+1)-Dimensional Spacetime Coupled to a Static Scalar Field

We use a generalized scheme of supersymmetric quantum mechanics to obtain the energy spectrum and wave function for Dirac equation in (1+1)-dimensional spacetime coupled to a static scalar field.     

Approximately analytical solutions of the Manning-Rosen potential with the spin-orbit coupling term and spin symmetry

In this Letter the approximately analytical bound state solutions of the Dirac equation with the Manning-Rosen potential for arbitrary spin-orbit coupling quantum number k are carried out by taking a properly approximate expansion for the spin-orbit coupling term. In the case of exact spin symmetry, the associated two-component spinor wave functions of the Dirac equation for arbitrary spin-orbit quantum number k are presented and the corresponding bound state energy equation is derived. We study briefly two special cases; the general s-wave problem and the equal scalar and vector Manning-Rosen potential.     

A GROUP OF EXACT (3+1) DIMENSIONAL CYLINDRICALLY SYMMETRIC WAVE SOLUTIONS TO THE EINSTEIN GRAVITATIONAL FIELD EQUATION

Starting with the diagonal spacetime metric tensor, the Einstein gravitational field equation is solved, and a set of exact (3+1) dimensional cylindrically symmetric wave solutions with two arbitrary functions are found. In these solutions all nonvanishing components of spacetime metric tensor are varying with the same propagating factor (ct-z) while the waves are travelling along z axis. The physical picture and the condition of positive energy density of the wave solutions are discussed.     

Approximate solution of Schr?dinger equation in D dimensions for inverted generalized hyperbolic potential

The Nikiforov?CUvarov method is used to investigate the bound state solutions of Schr?dinger equation with a generalized inverted hyperbolic potential in D-space. We obtain the energy spectrum and eigenfunction of this potential for arbitrary l-state in D dimensions. We show that the potential reduces to special cases such as Rosen?CMorse, Poschl?CTeller and Scarf potentials. The energy spectra and wave functions of these special cases are also discussed. The numerical results of these potentials are presented.     

Quantum corrections to ϕ 4 model solutions and applications to Heisenberg chain dynamics

The Heisenberg spin chain is considered in ? ⁴ model approximation. Quantum corrections to classical solutions of the one-dimensional ? ⁴ model within the correspondent physics are evaluated with account of rest d-1 dimensions of a d-dimensional theory. A quantization of the model is considered in terms of spacetime functional integral. The generalized zeta-function formalism is used to renormalize and evaluate the functional integral and quantum corrections to energy in a quasiclassical approximation. The results are applied to appropriate conditions of the spin chain model and its dynamics, for which elementary solutions, energy and the quantum corrections are calculated.     

O(d,d) symmetry in quantum cosmology

We analyze the quantum cosmology of one-loop string effective models which exhibit an O(d, d) symmetry. It is shown that due to the large symmetry of these models the Wheeler-de Witt equation can completely be solved. As a result, we find a basis of solutions with well-defined transformation properties under O(d, d) and under scale factor duality in particular. The general results are explicitly applied to 2-dimensional target spaces while some aspects of higher dimensional cases are also discussed. Moreover, a semiclassical wave function for the 2-dimensional black hole is constructed as a superposition of our basis.     

The classical field limit of scattering theory for non-relativistic many-boson systems. I

We study the classical field limit of non-relativistic many-boson theories in space dimensionn≧3. When ?→0, the correlation functions, which are the averages of products of bounded functions of field operators at different times taken in suitable states, converge to the corresponding functions of the appropriate solutions of the classical field equation, and the quantum fluctuations are described by the equation obtained by linearizing the field equation around the classical solution. These properties were proved by Hepp [6] for suitably regular potentials and in finite time intervals. Using a general theory of existence of global solutions and a general scattering theory for the classical equation, we extend these results in two directions: (1) we consider more singular potentials, (2) more important, we prove that for dispersive classical solutions, the ?→0 limit is uniform in time in an appropriate representation of the field operators. As a consequence we obtain the convergence of suitable matrix elements of the wave operators and, if asymptotic completeness holds, of theS-matrix.     

Approximate analytical solutions of the effective mass Dirac equation for the generalized Hulthén potential with any <Emphasis Type="Italic">κ</Emphasis>-value

The Dirac equation, with position-dependent mass, is solved approximately for the generalized Hulthén potential with any spin-orbit quantum number κ. Solutions are obtained by using an appropriate coordinate transformation, reducing the effective mass Dirac equation to a Schrödinger-like differential equation. The Nikiforov-Uvarov method is used in the calculations to obtain energy eigenvalues and the corresponding wave functions. Numerical results are compared with those given in the literature. Analytical results are also obtained for the case of constant mass and the results are in good agreement with the literature.     

Nonlinear quantum theory of interaction of charged particles and monochromatic radiation in a medium

We study the quantum theory of nonlinear interaction of charged particles and a given field of plane-transverse electromagnetic radiation in a medium. Using the exact solution of the generalized Lamé equation, we find the nonlinear solution of the Mathieu equation to which the relativistic quantum equation of particle motion in the field of a monochromatic wave in the medium reduces if one ignores the spin-spin interaction (the Klein-Gordon equation).We study the stability of solutions of the generalized Lamé equation and find a class of bounded solutions corresponding to the wave function of the particle. On the basis of this solution we establish that the particle states in a stimulated Cherenkov process form bands. Depending on the wave intensity and polarization, such a band structure describes both bound particle-wave states (capture) and states in the continuous spectrum. It is obvious that in a plasma there can be no such bands, since bound states of a particle with a transverse wave whose phase velocity v _ph is higher than c are impossible in this case. The method developed in the paper can be applied to a broad class of problems reducible to the solution of the Mathieu equation. Zh. éksp. Teor. Fiz. 113, 43–57 (January 1998)     

The Invariant-Relat ed Unitary Transformation Method and the Evolution of a Dirac Field in Friedmann-Robertson-Walker Flat Spacetimes

On the basis of the generalized invariant formulation, the invariant-related unitary transformation method is used to study the evolution of a quantum Dirac field in Friedmann-Robertson-Walker spatially flat spacetime. We first solve the functional Schrodinger equation for a free Dirac field and obtain the exact solutions. We then investigate the way of extending the method to treat the case in which there is an interaction between the Dirac field and a scalar field.     

Exact Time-Dependent Wave Functions of a Confined Time-Dependent Harmonic Oscillator with Two Moving Boundaries

By applying the standard analytical techniques of solving partial differential equations, we have obtained the exact solution in terms of the Fourier sine series to the time-dependent Schrödinger equation describing a quantum one-dimensional harmonic oscillator of time-dependent frequency confined in an infinite square well with the two walls moving along some parametric trajectories. Based upon the orthonormal basis of quasi-stationary wave functions, the exact propagator of the system has also been analytically derived. Special cases like (i) a confined free particle, (ii) a confined time-independent harmonic oscillator, and (iii) an aging oscillator are examined, and the corresponding time-dependent wave functions are explicitly determined. Besides, the approach has been extended to solve the case of a confined generalized time-dependent harmonic oscillator for someparametric moving boundaries as well.     

Gravity and duality between coordinates and matter fields

We use the duality between the local Cartezian coordinates and the solutions of the Klein-Gordon equation to parametrize locally the spacetime in terms of wave functions and prepotentials. The components of metric, metric connection, curvature as well as the Einstein equation are given in this parametrization. We also discuss the local duality between coordinates and quantum fields and the metric in this later reparametrization.     

Massless Spin–Zero Particle and the Classical Action via Hamilton–Jacobi Equation in G?del Universe

In this letter we investigate the separability of the Klein–Gordon and Hamilton–Jacobi equation in G?del universe. We show that the Klein–Gordon eigen modes are quantized and the complete spectrum of the particle’s energy is a mixture of an azimuthal quantum number, m and a principal quantum number, n and a continuous wave number k. We also show that the Hamilton–Jacobi equation gives a closed function for classical action. These results may be used to calculate the Casimir vacuum energy in G?del universe.     

Solutions of Dirac Equation in the Presence of Modified Tietz and Modified Poschl-Teller Potentials Plus a Coulomb-Like Tensor Interaction Using SUSYQM

The solutions of the Dirac equation with Modified Tietz and Modified Poschl-Teller scaler and vector potentials including the tensor interaction term for arbitrary spin-orbit quantum number κ are presented. We obtained the energy eigenvalues and the corresponding wave functions using the supersymmetry method. To show the accuracy of our results, we calculate the energy eigenvalues numerical for different values of n and κ. It is shown that these results are in good agreement with those found in the literature.     

The spin symmetry for deformed generalized Pöschl-Teller potential

In the case of spin symmetry we solve the Dirac equation with scalar and vector deformed generalized Pöschl-Teller (DGPT) potential and obtain exact energy equation and spinor wave functions for s-wave bound states. We find that there are only positive energy states for bound states in the case of spin symmetry based on the strong regularity restriction condition λ<−η for the wave functions. The energy eigenvalue approaches a constant when the potential parameter α goes to zero. Two special cases such as generalized PT potential and standard PT potential are also briefly discussed.     

A model of spontaneous symmetry breakdown in spatially flat cosmological spacetimes

This paper is an elaboration of a previous short exposition of a theory of spontaneous symmetry breaking in a conformally coupled, massless λø⁴ model in a spatially flat Robertson-Walker spacetime. Under the weakened global boundary condition allowing the physical spacetime to be conformal to only a portion of the Minkowski spacetime, the model admits a pair of degenerate vacua in which the ø → ? ø symmetry is spontaneously broken. The model is formulated as a euclidean field theory in a space with a positive-definite metric obtained by analytically continuing the conformal time coordinate. An appropriate time-dependent zero energy solution of the euclidean equation of motion representing the field configuration in the asymmetric vacuum is considered and the corresponding quantum trace anomaly 〈T_μ^μ〉 is computed in the one-loop approximation. The nontrivial infrared behavior of the model due to the singular nature of the classical background field forces a modification of the boundary conditions on the propagator. A general form for an “improved|DD one-loop trace anomaly is found by a simple argument based on renormalization group invariance. Via the Einstein equation, the trace anomaly leads to a self-consistent dynamical equation for the cosmic expansion scale factor. Some physical aspects of the back-reaction problem based on a simple power law model of the expansion scale factor are discussed.     

Solutions of Dirac Equation for Generalized Hyperbolical Potential Including Coulomb-Like Tensor Potential with Spin Symmetry

We solved the Dirac equation for the generalized hyperbolical potential including a Coulomb-like tensor potential under spin symmetry with spin-orbit quantum number k. We used the parametric generalization of the Nikiforov–Uvarov method to obtain the energy eigenvalue and the unnormalized wave function.