Two-sided estimates for eigenvalues of the Schrödinger equation

G. V. Ryazanov


Abstract: 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.

Received: 26.12.1974

 English version: Theoretical and Mathematical Physics, 1975, 24:3, 926–930

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