Solution of an analogous Schrödinger equation for

PT-symmetric sextic potential in two dimensions

FAKIR CHAND^1,*, S C MISHRA¹ and RAM MEHAR SINGH²

¹Department of Physics, Kurukshetra University, Kurukshetra 136 119, India

²Department of Physics, Ch. Devi Lal University, Sirsa 125 055, India

^*Corresponding author. E-mail: fchand72kuk@gmail.com

Abstract. We investigate the quasi-exact solutions of an analogous

Schr\"odinger wave equation for two-dimensional non-Hermitian

complex Hamiltonian systems within the framework of an extended

complex phase space characterized by $x=x_1+ip_3, y=x_2+ip_4,

p_x=p_1+ix_3, p_y=p_2+ix_4$. Explicit expressions for the energy

eigenvalues and eigenfunctions for ground and first excited states

of a two-dimensional PT-symmetric sextic potential and

some of its variants are obtained. The eigenvalue spectra are found

to be real within some parametric domains.

Keywords. Schr\"odinger equation; complex Hamiltonian; PT

symmetry; eigenvalues and eigenfunctions.

PACS No. 03.65.Ge