Degenerate trajectories and Hamiltonian envelopes in the method of self-similar approximations

Abstract

We study two new techniques for the approximate calculation of the eigenvalues of the Schrödinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one of the authors. We illustrate the ideas by an anharmonic oscillator problem. We show that the precision of the method can be very high. For example, the ground-state energy of an anharmonic oscillator can be calculated with an error not exceeding 0.07% for all anharmonicity parameters ranging from zero to infinity.