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Considering our expanding universe as made up of gravitationally interactingparticles which describe particles of luminous matter and dark matter and darkenergy which is described by a repulsive harmonic potential among the points inthe flat 3-space, we derive a quantum mechanical relation connecting,temperature of the cosmic microwave background radiation, age, and cosmologicalconstant of the universe. When the cosmological constant is zero, we get backthe Gamow's relation with a much better coefficient. Otherwise, our theorypredicts a value of the cosmological constant $2.0 10^{-56} {\rm {cm^{-2}}}$when the present values of cosmic microwave background temperature of 2.728 Kand age of the universe 14 billion years are taken as input.Comment: 4 pages, 1 figure, Study of the Universe from a condensed matter  point of view, section III corrected with a single body potentia

A Quantum Mechanical Relation Connecting Time, Temperature, and Cosmological Constant of the Universe: Gamow’S Relation Revisited as a Special Case