DEGENERATE TRAJECTORIES AND HAMILTONIAN ENVELOPES IN THE METHOD OF SELF-SIMILAR APPROXIMATIONS

We study two new techniques for the approximate calculation of the eig envalues of the Schrodinger equation. These techniques are variants of the method of self-similar approximations suggested recently by one o f the authors. We illustrate the ideas by an anharmonic oscillator pro blem. We show that the precision of the method can be very high. For e xample, the ground-state energy of an anharmonic oscillator can be cal culated with an error not exceeding 0.07% for all anharmonicity parame ters ranging from zero to infinity.