Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 78

The Hamiltonian operator Ĥ we consider is the sum of operators for the kinetic energy , the one-body potential energy , and the interaction energy :

(1)

The first term is simply the sum of the individual kinetic energy operators associated with each of the particles q:

(2)

where:

(3)

(P_q is the momentum of particle q). Similarly, is the sum of the external potential operators V₁(R_q), each depending on the position operator R_q of particle q:

(4)

Finally, is the sum of the interaction energy associated with all the pairs of particles:

(5)

(this summation can also be written as a sum over q < q′, while removing the prefactor 1/2).