Suppose two orthogonal neighbouring orbitals ##|\phi _1 \rangle## and ##|\phi _2 \rangle## so that ##\langle \phi_1|\phi _2 \rangle =0##. Applying an electric field adds a new term ##u (c_1^{\dagger}c_1-c_2^{\dagger}c_2)## to the Hamiltonian which u is a constant potential. Obviously, we still...