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Algebraic approach to the Hulthen potential
In this paper the energy eigenvalues and the corresponding eigenfunctions are
calculated for Hulthen potential. Then we obtain the ladder operators and show
that these operators satisfy SU(2) commutation relation.Comment: 8 Pages, 1 Tabl
Size growth of red-sequence early-type galaxies in clusters in the last 10 Gyr
We carried out a photometric and structural analysis in the rest-frame
band of a mass-selected () sample of red-sequence
galaxies in 14 galaxy clusters, 6 of which are at . To this end, we
reduced/analyzed about 300 orbits of multicolor images taken with the Advanced
Camera for Survey and the Wide Field Camera 3 on the Hubble Space Telescope. We
uniformly morphologically classified galaxies from to , and
we homogeneously derived sizes (effective radii) for the entire sample.
Furthermore, our size derivation allows, and therefore is not biased by, the
presence of the usual variety of morphological structures seen in early-type
galaxies, such as bulges, bars, disks, isophote twists, and ellipiticy
gradients. By using such a mass-selected sample, composed of 244 red-sequence
early-type galaxies, we find that the of the galaxy size at a fixed
stellar mass, has increased with time at a rate of
dex per Gyr over the last 10 Gyr, in marked contrast with the
threefold increase found in the literature for galaxies in the general field
over the same period. This suggests, at face value, that secular processes
should be excluded as the primary drivers of size evolution because we observed
an environmental environmental dependent size growth. Using spectroscopic ages
of Coma early-type galaxies we also find that recently quenched early-type
galaxies are a numerically minor population not different enough in size to
alter the mean size at a given mass, which implies that the progenitor bias is
minor, i.e., that the size evolution measured by selecting galaxies at the
redshift of observation is indistinguishable from the one that compares
ancestors and descendents.Comment: A&A 593, A2 (2016) after revision of the z=1.63 cluster name,
mis-typed in previous version. No result of our paper is affected by having
mis-typed the cluster nam
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