Cooper Pairs in Alternating Layers of Light and Heavy Atoms

The Hamiltonian and trial function in the BCS theory are improved to test the limit of this theory. The Cooper pairs arise from standing electron waves, ready to move with atoms, giving high Tc. The Hamiltonian is derived from alternating layers of light and heavy atoms, giving a forbidden zone hosting no standing wave pairs. The exchange term may force singlet pairs into this zone, leaving triplet pairs outside, giving magnetic excitations. If the Fermi energy is crossed only by the CuO2 band, then the forbidden zone and triplet pairs will vanish, consistent with experimental evidence.