Ψ$_{t}$ in the three terms of Eq. (13) can be considered formal since, due to the short-range character of the integral relations, it is sufficient for the trial wave function to be a solution of ( H − E )Ψ$_{t}$ = 0 in the interaction region, without an explicit indication of its asymptotic behavior. This fact, together with the variational character of the relations, allows for a number of applications to be discussed in the next sections. In this section we present applications of the integral relations of Eq. (21) to a two-body system. To make contact with the results given in Refs. [22, 23], we use a central, s -wave gaussian potential with V$_{0}$ = − 51 . 5 MeV, r$_{0}$ = 1 . 6 fm and ℏ $^{2}$/m = 41 . 4696 MeV fm $^{2}$. This potential has a shallow L = 0 bound state with energy E$_{2}$$_{B}$ = − 0 . 397743 MeV. We introduce the orthogonal basis with L m a (normalized) Laguerre polynomial and z = βr , where β is a nonlinear parameter, to expand the wave function of the system We solve the eigenvalue problem of H for different dimensions M of the basis. The variational principle states that with the equality valid when M → ∞ . The nonlinear parameter β can be fixed to improve the convergence properties of the basis. In fact, for each value of M there is a value of β that minimizes the energy. Increasing M , the minimum of the energy becomes less and less dependent on β resulting in a plateau. Increasing further the dimension of the basis, the extension of the plateau increases as well, without any appreciable improvement in the eigenvalue, indicating that the convergence has been reached to a certain accuracy. At each step Ψ$_{0}$ represents a first order estimate of the exact bound state wave function. 8 E$_{0}$ = 〈 Ψ$_{0}$ | H | Ψ$_{0}$ 〉 ≥ E$_{2}$$_{B}$ , (25) Ψ$_{0}$ = $^{M}$− 1 ∑ m =0 a 0 $_{m}$φ$_{m}$ . (24) φ$_{m}$ = L (2) m ( z ) exp − ( z/ 2) , (23) V ( r ) = − V$_{0}$ exp ( − r $^{2}$/r2 $_{0}$) , (22) III. USE OF THE INTEGRAL RELATIONS IN THE TWO-BODY CASE