Energy Spectrum of a 2D Dirac Oscillator in the Presence of the Aharonov-Bohm Effect

We determine the energy spectrum and the corresponding eigenfunctions of a 2D Dirac oscillator in the presence of Aharonov-Bohm (AB) effect . It is shown that the energy spectrum depends on the spin of particle and the AB magnetic flux parameter. Finally, when the irregular solution occurs it is shown that the energy takes particular values. The nonrelativistic limit is also considered.Comment: Latex, 12 page

Klein's Paradox

We solve the one dimensional Feshbach-Villars equation for spin-1/2 particle subjected to a scalar smooth potential. The eight component wave function is given in terms of the hypergeometric functions and via a limiting procedure, the wave functions of the step potential are deduced. These wave functions are used to test the validity of the boundary conditions deduced from the Feshbach-Villars transformation. The creation of pairs is predicted from the boundary condition of the charge density.Comment: 18 pages, Latex, another title has been used in the published versio

Cosmological consequences of a variable cosmological constant model

We derive a model of dark energy which evolves with time via the scale factor. The equation-of-state is studied as a function of a parameter α introduced in this model as = (1 - 2α)/(1 + 2α). In addition to the recent accelerated expansion, the model predicts another decelerated phase. These two phases are studied via the parameter α. The age of the universe is found to be almost consistent with the observation. In the limiting case, the cosmological constant model, we find that vacuum energy gravitates with a tiny gravitational constant which evolves with the scale factor, rather than with Newton's constant. This enables degravitation of the vacuum energy which in turn produces the tiny observed curvature, rather than a 120 orders of magnitude larger value

Exact solutions for time-dependent complex symmetric potential well

Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left(x,t\right)=if\left(t\right)\left\vert x\right\vert$. The problem is exactly solvable and the analytic expressions of the Schr\"{o}dinger wavefunctions are given in terms of the Airy function. Indeed, with an appropriate choice of the time-dependent metric operators and the unitary transformations, for each region, the two corresponding pseudo-Hermitian invariants transform into a well-known time-independent Hermitian invariant which is the Hamiltonian of a particle of unit mass confined in a symmetric potential well. The eigenfunctions of the last invariant are the Airy functions. Then the phases obtained are real for both regions and the general solution of the problem deduced.Comment: 14 page