Atmospheric Neutrino Problem in Maximally-Mixed Three Generations of Neutrinos

Motivated by the indication that both the atmospheric and the solar neutrino puzzles may simultaneously be solved by (vacuum as well as matter-induced resonant) oscillations of two generations of neutrinos with large mixing, we have analyzed the data on the atmospheric and solar neutrinos assuming that all {\it three} neutrinos are maximally mixed. It is shown that the values of $\mathrm{\Delta }{m}^2$ obtained from the two-generation analyses are still valid even in the three-generation scheme, i.e. the two puzzles can be solved simultaneously if $\mathrm{\Delta }{m}_{31}^2\simeq {10}^{-2}{\mathrm{e}\mathrm{V}}^2$ for the atmospheric neutrinos and $\mathrm{\Delta }{m}_{21}^2\simeq {10}^{-10}{\mathrm{e}\mathrm{V}}^2$ for solar neutrinos in the maximally mixed three-generation scheme.