Solution of the Schroedinger equation with one and two dimensional   double-well potentials
  The Schroedinger equation with one and two dimensional potentials are solved in the frame work of the sl(2) Lie algebra. Eigenfunctions of the Schroedinger equation for various asymmetric double-well potentials have been determined and the eigenstates are expressed in terms of the orthogonal polynomials. The solution of the double-well potential in two dimension have been analyzed. 
Ramazan Koc and Derya Haydargil