Kinetic energy bounds for particles confined in spherically-symmetric traps with non-standard dimensions

The kinetic energy of non-relativistic single-particle systems with arbitrary D-dimensional central potentials is found to be bounded from below by means of the orbital hyperangular quantum number, the dimensionality and some radial and logarithmic expectation values of the form langrkrang and langrk (ln r)mrang. Beyond the intrinsic physico-mathematical interest of this problem, we want to contribute to the current development of the theory of independent particles confined in spherically symmetric traps with non-standard dimensions. The latter has been motivated by the recent experimental achievements of the evaporative cooling of dilute (i.e. almost non-interacting) fermions in magnetic traps.We are very grateful for partial support from Junta de Andalucía (under the grants FQM-0207 and FQM-481), Ministerio de Educación y Ciencia (under the project FIS2005-00973), and the European Research Network NeCCA (under the project INTAS-03-51-6637). RGF acknowledges the support of Junta de Andalucía under the program of Retorno de Investigadores a Centros de Investigación Andaluces, and PSM the support of Ministerio de Educación y Ciencia under the program FPU