Two-sided estimates for eigenvalues of the Schrödinger equation

Schrödinger equation is substituted into two systems of $n$ linear equations with $n$ unknown quantitys. The coefficients of these equations are the matrix elements of the hamiltonian between quasiclassical wavefunctions. The solution of these systems give the two-side estimates for eigenvalues of the Schrodinger equation. The relative distance between boundary $\simeq\lambda^k$, where $\lambda$ is the parameter of the quasiclassical decomposition for the $n$-th wavefunction, $k$ is the number of terms in this decomposition.