Announcement iconContinuing Accepting Applications for Admission !!
for the Spring Semester of the Academic Year 2019/2020

Studying The Linear Complex Pt Symmetric Potential

Journal: 
Journal of the Arab American University, Volume 5, Issue 1, 2019
Pages: 
12-21
Abstract: 

We investigate the spectrum of the linear complex PT symmetric potential V(x) = λ|x| + icx. Semi analytical solutions are given by using properties of the Airy functions. The numerical integration of the differential equation system is discussed. We show that the number of eigenstates with a real eigenvalue is limited, depending on the ratio c/λ and on the quantum number n, reflecting a spontaneous breaking of the PT symmetry. For the ground state ( n = 0), we conjecture the eigenvalue to be real whatever the value of c.

Keywords: 

Airy function, Complex symmetric potential.