Solution of an analogous Schrödinger equation for $mathcal{PT}$-symmetric sextic potential in two dimensions

Pramana

S C Mishra¹  Fakir Chand1¹  Ram Mehar Singh² 

[1] Department of Physics, Kurukshetra University, Kurukshetra 136 119, India$$;Department of Physics, Ch. Devi Lal University, Sirsa 125 055, India$$

关键词: Schrödinger equation;    complex Hamiltonian;    $mathcal{PT}$ symmetry;    eigenvalues and eigenfunctions.;   

DOI  :  

学科分类：物理（综合）

来源: Indian Academy of Sciences

【 摘 要 】

We investigate the quasi-exact solutions of an analogous Schrödinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by 𝑥 = 𝑥1 + 𝑖𝑝3, 𝑦 = 𝑥2 + 𝑖𝑝4, 𝑝𝑥 = 𝑝1 + 𝑖𝑥3, 𝑝𝑦 = 𝑝2 + 𝑖𝑥4. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional $mathcal{PT}$-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.

【 授权许可】

Unknown