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.
We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators H(t) that generate a real phase in their time-evolution. This involves the use of invariant operators I P H (t) that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore, H(t) is generally not quasi-Hermitian and does not define an observable of the system but I P H (t) obeys a quasi-hermiticity transformation as in the completely timeindependent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.
We show that the description of the space-time of general relativity as a diagonal four dimensional submanifold immersed in an eight dimensional hypercomplex manifold, in torsionless case, leads to a geometrical origin of the cosmological constant. The cosmological constant appears naturally in the new field equations and its expression is given as the norm of a four-vector U , i.e., Λ = 6g µν U µ U ν and where U can be determined from the Bianchi identities. Consequently, the cosmological constant is space-time dependent, a Lorentz invariant scalar, and may be positive, negative or null. The resulting energy momentum tensor of the dark energy depends on the cosmological constant and its first derivative with respect to the metric. As an application, we obtain the spherical solution for the field equations. In cosmology, the modified Friedmann equations are proposed and a condition on Λ for an accelerating universe is deduced. For a particular case of the vector U , we find a decaying cosmological constant Λ ∝ a(t)
Using the Lewis–Riesenfeld theory, we show that the time-dependent Schrödinger equation for non-central potentials with an arbitrary angular function U(θ) is analytically solvable. As a special case, we derive the exact solution for the double ring-shaped generalized non-central oscillator with time-dependent mass and frequency. The time-independent case, studied in the literature, is recovered.
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