Quantum Mechanics of Complex Sextic Potentials in One Dimension

Abstract

Within the framework of an extended complex phase space approach characterized by x = x1 + ip2, p = p1 + ix2, we investigate the quasi-exact solutions of an analogous Schrödinger equation for a variety of complex sextic potentials of the type V(x) = a + bx + cx2 + dx3 + ex4 + fx5 + hx6 with complex couplings. It is found that the eigenvalue spectrum in general is complex for complex couplings and real for the real parameters of the potential. While the ground state solutions for an even power sextic potential with an inverse harmonic term and for the - symmetric version of V(x) are obtained, other variants of V(x) are also investigated with reference to the excited states.