114 research outputs found
On solvable Dirac equation with polynomial potentials
One dimensional Dirac equation is analysed with regard to the existence of
exact (or closed-form) solutions for polynomial potentials. The notion of
Liouvillian functions is used to define solvability, and it is shown that
except for the linear potentials the equation in question is not solvable.Comment: 3 pages, updated bibliograph
Exact solutions for Big Bounce in loop quantum cosmology
In this paper we study the flat (k=0) cosmological FRW model with holonomy
corrections of Loop Quantum Gravity. The considered universe contains a
massless scalar field and the cosmological constant Lambda. We find analytical
solutions for this model in different configurations and investigate its
dynamical behaviour in the whole phase space. We show the explicit influence of
Lambda on the qualitative and quantitative character of solutions. Even in the
case of positive Lambda the oscillating solutions without the initial and final
singularity appear as a generic case for some quantisation schemes.Comment: 12 pages, 12 figures, added references and changed introduction and
summar
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