  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.
