The solution of the Schr??dinger equation for coupled quadratic and quartic potentials in two dimensions

摘要

We deal with the difficulties claimed by the author of [Ann. Phys. 206, 90 (1991)] while solving the Schr??dinger equation for the ground states of two-dimensional anharmonic potentials. It is shown that the ground state energy eigenvalues and eigen-functions for the coupled quadratic and quartic potentials can be obtained by making some simple assumptions. Expressions for the energy eigenvalues and the eigenfunctions for the first and second excited states of these systems are also obtained.