Operator method in the problem of quantum anharmonic oscillator
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.
nonperturbative method of the Schrödinger equation solution
analytical interpolation for eigenfunctions and eigenvalues of the Hamiltonian
scientific article; zbMATH DE number 727784