Operator method in the problem of quantum anharmonic oscillator

Journal Article · Wed Mar 01 04:00:00 EST 1995 · Annals of Physics (New York)

DOI:https://doi.org/10.1006/aphy.1995.1025· OSTI ID:102922

Feranchuk, I D; Komarov, L I; Nichipor, I V ^[1]

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1. Byelorussian State Univ., Minsk (Russian Federation); and others

The problem of quantum anharmonic oscillator is considered as a test for a new non-perturbative method of the Schroedinger equation solution-the operator method (OM). It is shown that the OM zeroth-order approximation permits us to find such analytical inter-polation for eigenfunctions and eigenvalues of the Hamiltonian which ensures high accuracy within the entire range of the anharmonicity constant changing and for any quantum numbers. The OM subsequent approximations converge quickly to the exact solutions of the Schroedinger equation. These results are justified for the different types of anharmonicity (double-well potential, quasistationary states, etc.) and can be generalized for more complicated quantum-mechanical problems. 87 refs., 10 figs., 14 tabs.

• OSTI ID: 102922
• Journal Information: Annals of Physics (New York), Journal Name: Annals of Physics (New York) Journal Issue: 2 Vol. 238; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ANALYTICAL SOLUTION
ANHARMONIC OSCILLATORS
HAMILTONIAN FUNCTION
MATHEMATICAL OPERATORS
QUANTUM MECHANICS
SCHROEDINGER EQUATION