Studying The Linear Complex Pt Symmetric Potential

Authors

Roland Lombard, Université de Boumerdes- AlgeriaFollow

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.

Recommended Citation

Lombard, Roland (2019) "Studying The Linear Complex Pt Symmetric Potential," Journal of the Arab American University مجلة الجامعة العربية الامريكية للبحوث: Vol. 5: Iss. 1, Article 2.
Available at: https://digitalcommons.aaru.edu.jo/aaup/vol5/iss1/2