Collect. Czech. Chem. Commun. 2008, 73, 1327-1339

Analytic Energies and Wave Functions of Two-Dimensional Schrödinger Equation: Two-Dimensional Fourth-Order Polynomial Potential

Vladimír Tichýa and Lubomír Skálab,a,*

a Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 121 16 Prague 2, Czech Republic
b Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1


Direct method for searching analytic solutions of the two-dimensional Schrödinger equation with a two-dimensional fourth-order polynomial potential is presented. Analytic formulas for the energies and wave functions of the ground state and excited state are found. Obtained results can not be in general reduced to two one-dimensional cases.

Keywords: Analytic solution; Anharmonic oscillator; Polynomial potential; Schrödinger equation; Quantum chemistry.

References: 14 live references.