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

Abstract

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.