Spatial Distributions

In Chap. 2 , we discussed the fundamental molecular interactions, which can be represented approximately as classical potentials V . These potentials appear in a classical treatment (Hamiltonian formalism) of the Hamiltonian function \(H = T +V\) , that represents the total energy of a system. Its counterpart in quantum mechanics is the Hamiltonian operator. Operating on the wavefunction with the Hamiltonian produces the Schrödinger equation. In the time independent Schrödinger equation, the operation produces specific values for the energy called energy eigenvalues \(E_n\) . In the calculation of the state sumQ, the exponent is either H or the eigenenergies \(E_n\) : In both cases the potentials must be very simple to get compact solutions.