Читать книгу Quantum Mechanics, Volume 3 - Claude Cohen-Tannoudji - Страница 137

We assume the N-particle state vector to be of the form:

(1)

where the are the creation operators associated with an arbitrary series of orthonormal individual states |θ₁(t)〉, |θ₂(t)〉, …, |θN(t)〉 which depend on time t. This series is, for the moment, arbitrary, but the aim of the following variational calculation is to determine its time dependence.

As in the previous complements, we assume that the Hamiltonian Ĥ is the sum of three terms: a kinetic energy Hamiltonian, an external potential Hamiltonian, and a particle interaction term:

(2)

with:

(3)

(m is the particles’ mass, P_q the momentum operator of particle q), and:

(4)

and finally:

(5)