Operator method in the problem of quantum anharmonic oscillator
type: Item
instance of: scholarly article
title: Operator method in the problem of quantum anharmonic oscillator
zbMATH Open document ID: 0815.47079
author: I. D. Feranchuk
author: L. I. Komarov
author: I. V. Nichipor
author: Alexander Ulyanenkov
published in: Annals of Physics
publication date: 1995-03-02T00:00:00Z
review text: The problem of quantum anharmonic oscillator is considered as a test for a new nonperturbative method of the Schrödinger equation solution -- the operator method (OM). It is shown that the OM zeroth-order approximation permits us to find such analytical interpolation 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 Schrödinger equation. These results are justified for different types of anharmonicity (double-well potential, quasistationary states, etc.) and can be generalized for more complicated quantum-mechanical problems.
Mathematics Subject Classification ID: 47N50
Mathematics Subject Classification ID: 81Q05
zbMATH DE Number: 727784
zbMATH Keywords: double-well potential
zbMATH Keywords: quantum anharmonic oscillator
zbMATH Keywords: nonperturbative method of the Schrödinger equation solution
zbMATH Keywords: operator method
zbMATH Keywords: analytical interpolation for eigenfunctions and eigenvalues of the Hamiltonian
zbMATH Keywords: quasistationary states
MaRDI profile type: Publication
full work available at URL: aphy.1995.1025
OpenAlex ID: W2042903222
DOI: 10.1006/APHY.1995.1025
description: scientific article; zbMATH DE number 727784