Nonlinear Phenomena in Complex Systems, 2013, Vol.16, No.3, pp.217-231

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2013, Vol.16, No.3, pp.217-231

Operator Method for Nonperturbative Description of Quantum Systems
I.Feranchuk, A. Ivanov, and A. Ulyanenkov

Nonperturbative method for description of quantum systems - the operator method (OM) and the conception of the uniformly suitable estimation (USE) are considered for the series of real physical systems. It is shown that the OM zeroth-order approximation permits one to find the analytical approximation for eigenfunctions and eigenvalues with high accuracy within the entire range of the Hamiltonian parameters and any quantum numbers. The OM subsequent approximations converge rapidly to the exact solutions of the Schr¨odinger equation. The generalization of OM for the quantum statistics is also developed.

Key words: nonperturbative method, operator method, quantum statistics, anharmonicity, uniformly suitable estimation

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