.

The Exchange Integral (Between Carbons 1-2 and 3-4)

The matrix element of the Hamiltonian connecting these two orbitals would be

$$H_{1-2} = H_{2-1} = \int p_1 H p_2 d\tau= \int \left (\left ... ...a_{1-2} + p_y cos \theta_{1-2} \right )_1 \right ) H p_K d\tau$$