Eigenvalue spectra of a <Emphasis Type="Italic">PT</Emphasis>-symmetric coupled quartic potential in two dimensions

The Schrödinger equation was solved for a generalized PT-symmetric quartic potential in two dimensions. It was found that, under a suitable ansatz for the wave function, the system possessed real and discrete energy eigenvalues. Analytic expressions for the energy eigenvalues and the eigenfunctions for the first four states were obtained. Some constraining relations among the wave function parameters rendered the problem quasi-solvable.