The quartic oscillator

The quantum quartic oscillator is treated on the basis of a singularity-analytic approach to the central two-point connection problem of the triconfluent case of Heun close-quote s differential equation. We split off the asymptotic factors by means of a specific linear transformation of the independent variable and represent the solution in terms of a Jaffacute e expansion. The result is a fourth-order linear difference equation of Poincaracute e endash Perron type the asymptotic behavior of which is significant for the connection problem. This is investigated by means of the Birkhoff-set of the difference equation and leads to the exact eigenvalue-condition of the problem. copyright 1997 American Institute of Physics