Quasiaccurately solvable quantum mechanics problems and the anharmonic oscillator problem

The basic methods of obtaining the anharmonic oscillator spectrum are briefly reviewed. An approach is discussed to this problem from the point of view of one of the quasiaccurately solvable models of quantum mechanics, whose wave functions are applicable to the construction of a regular perturbation theory. Results are presented of numerical calculations of the ground state energy. Analytic calculations are provided of integrals of the form , occurring in applications of the method of quasiaccurately solvable problems. M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 76–88, February, 1993.