K-Inflation in Noncommutative Space-Time

The power spectra of the scalar and tensor perturbations in the noncommutative k-inflation model are calculated in this paper. In this model, all the modes created when the stringy space-time uncertainty relation is satisfied are generated inside the sound/Hubble horizon during inflation for the scalar/tensor perturbations. It turns out that a linear term describing the noncommutative space-time effect contributes to the power spectra of the scalar and tensor perturbations. Confronting the general noncommutative k-inflation model with latest results from \textit{Planck} and BICEP2, and taking $c_S$ and $\lambda$ as free parameters, we find that it is well consistent with observations. However, for the two specific models, i.e. the tachyon and DBI inflation models, it is found that the DBI model is not favored, while the tachyon model lies inside the $1\sigma$ contour, if the e-folds number is assumed to be around $50\sim60$.Comment: 9 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1404.016

Connection between closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation

It was shown that the Runge-Lenz vector for a hydrogen atom is equivalent to the raising and lowering operators derived from the factorization of radial Schr\"{o}dinger equation. Similar situation exists for an isotropic harmonic oscillator. It seems that there may exist intimate relation between the closeness of classical orbits and the factorization of radial Schr\"{o}dinger equation. Some discussion was made about the factorization of a 1D Schr\"{o}dinger equation.Comment: 14 pages, no figure