Analytic energies and wave functions of the two-dimensional Schrodinger equation: ground state of two-dimensional quartic potential and classification of solutions

Abstract

New analytic solutions of the two-dimensional Schrodinger equation with a two-dimensional fourth-order polynomial (i.e., quartic) potential are derived and discussed. The solutions represent the ground state energies and the corresponding wave functions.

In general, the obtained results cannot be reduced to two one-dimensional cases.

Keywords

• Schrodinger equation
• partial differential equation
• analytic solution
• anharmonic oscilator
• double-well