Rz. Zhdanov et al., ON THE NEW APPROACH TO VARIABLE SEPARATION IN THE TIME-DEPENDENT SCHRODINGER-EQUATION WITH 2 SPACE DIMENSIONS, Journal of mathematical physics, 36(10), 1995, pp. 5506-5521
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.