ON THE NEW APPROACH TO VARIABLE SEPARATION IN THE TIME-DEPENDENT SCHRODINGER-EQUATION WITH 2 SPACE DIMENSIONS

We suggest an effective approach to separation of variables in the Sch rodinger equation with two space variables. Using it we classify inequ ivalent potentials V(x(1)x(2)) such that the corresponding Schrodinger equations admit separation of variables. Besides that, we carry out s eparation of variables in the Schrodinger equation with the anisotropi c harmonic oscillator potential V = k(1)x(1)(2) + k(2)x(2)(2) and obta in a complete list of coordinate systems providing its separability. M ost of these coordinate systems depend essentially on the form of the potential and do not provide separation of variables in the free Schro dinger equation (V = 0). (C) 1995 American Institute of Physics.