We seek a possible room temperature superconductivity beyond the Cooper pairing mechanism through quartet condensation. A quartet consists of two kinds of electron pairs of a spin singlet with total momenta zero belonging to two different bands. We calculate the ground state energy, the energy gap, the excited state energy and the transition temperature by extending the BCS theory for pairing condensation to quartet condensation for a possible room temperature transition to superconductivity.

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... do this for a two-band electron system rather than for the ordinary superconductor of a single-band electron, because the effective interaction is larger in this case than in the case of the pairing interaction. We conjecture that the idea of the quartet condensation may be applicable to superfluid 4 He.