ON THE QUANTUM ANHARMONIC OSCILLATOR AND PADE APPROXIMATIONS

For the quantum quartic anharmonic oscillator with the Hamiltonian H = 1/2 (p(2) + x(4)) + lambda x(4), which is one of the traditional quantum-mechanical and quantum-field-theory models, we study summation of its factorially divergent perturbation series by the proposed method of averaging of the corresponding Pade approximants. Thus, for the first time, we are able to construct the Pade-type approximations that possess correct asymptotic behaviour at infinity with a rise of the coupling constant lambda. The approach gives very essential theoretical and applicatory-computational advantages in applications of the given method. We also study convergence of the applied approximations and calculate by the proposed method the ground state energy E-0(lambda) of the anharmonic oscillator for a wide range of variation of the coupling constant lambda.