Solution of the Schrödinger equation with one and two dimensional double-well potentials

Özet

The Schrödinger equation with one and two dimensional potentials are solved in the framework of the $sl_2(R)$ Lie algebra. Eigenfunctions of the Schrödinger 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.