OPERATOR METHOD IN THE PROBLEM OF QUANTUM ANHARMONIC-OSCILLATOR

The problem of quantum anharmonic oscillator is considered as a test f or a new nonperturbative method of the Schrodinger equation solution-t he operator method (OM). It is shown that the OM zeroth-order approxim ation permits us to find such analytical interpolation for eigenfuncti ons and eigenvalues of the Hamiltonian which ensures high accuracy wit hin the entire range of the anharmonicity constant changing and for an y quantum numbers. The OM subsequent approximations converge quickly t o the exact solutions of the Schrodinger equation. These results are j ustified for different types of anharmonicity (double-well potential, quasistationary states, etc.) and can be generalized for more complica ted quantum-mechanical problems. (C) 1995 Academic Press, Inc.