No abstract

In this paper, the plane wave solutions of a free particle in three dimensions for Cubical and Spherical Symmetry have been considered. The coordinate space wave functions for the Cubical and Spherical Symmetry are obtained by solving the Schrdinger differential equation. The momentum space wave function is obtained by using the operator form of an observable in the case of Cubical Symmetry. For Spherical Symmetry, the same is obtained by taking the Fourier transform of the respective coordinate space wave function. The wave functions have been used to constitute probability densities in coordinate and momentum space for both the symmetries. Further, the Shannon information entropy has been computed both in coordinate and momentum space respectively for  (L is the length of the side of the cubical box) values for Cubical Symmetry and for  values in Spherical Symmetry keeping (k is the wave vector and p is the momentum of the free particle) constant. The values obtained for the Shannon information entropies are found to satisfy the Bialynicki-Birula and Myceilski (BBM) inequality at larger  values () in case of Cubical Symmetry and for values of  and  in Spherical Symmetry.

Teleparallel gravity theories were proposed as alternatives to the dark energy and modified theories of gravity. However, both the metric and symmetric teleparallel gravity theories have been found to have serious pathologies, such as coupling issues and Ostrogradski's instability leading to ghost degrees of freedom. In this article we explore the fact that the theories are at-least free from the issue of 'Branched Hamiltonian' though, nonetheless, early inflation as well as a viable radiation era may only be driven by a scalar field.