Eigenvalue spectra of a PT-symmetric coupled quartic potential in two dimensions

Zafar Ahmed

Zafar Ahmed, D. C. Ghosh, Joseph Amal Nathan +1 more

Axel Schulze‐Halberg, Pinaki Roy

Ram Mehar Singh, Fakir Chand, Shubham Mishra

We investigate the quasi-exact solutions of the Schr?dinger wave equation for two-dimensional non-hermitian complex Hamiltonian systems within the frame work of an extended complex phase space characterized by x = x1 + ip3, y = x2 + ip4, px = p1 + ix3, py = p2 + ix4. Explicit expressions of the energy eigenvalues and the eigenfunctions for ground and first excited states for a complex quartic potential are obtained. Eigenvalue spectra of some variants of the complex quartic potential, including PT-symmetric one, are also worked out.

Avinash Khare, Bhabani Prasad Mandal

Alexandre Eremenko, Andrei Gabrielov

We describe a parametrization of the real spectral locus of the two-parametric family of PT-symmetric quartic oscillators. For this family, we find a parameter region where all eigenvalues are real, extending the results of Dorey et al (2007 J. Phys. A: Math Theor. 40 R205–83) and Shin (2005 J. Phys. A: Math. Gen. 38 6147–66; 2002 Commun. Math. Phys. 229 543–64).